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-JUN 2 11~989
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FUNDAMENTAL MECHANISMS OF TRIBOLOGY
AND THEIR IMPLICATIONSI (ONR Contract No. NOOO4-82-K-0520)
by
N. P. Suh, N. Saka and K. Komvopoulos
May 1989II£
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D1.strwuuenUzlwiiIt I 1
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I UnclassifiedSEC iR '
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68. NAME OF PERFORMING ORGANIZA'rtON 6b OFF1CE SYMBOL 7a NAME OF MONITORING ORGANIZATIONMassachusetts Institute of (if applicable) Office of Naval ResearchTechnology I _---_I
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N00014 -82-K -0520 091-03211 TITLE (Include Security Classficarion)
Fundamental Mechanisms of Tribology and Their Implications
12 PERSONAL AU T HOR(S) Nam P. Suh, Nannaji Saka and Kyriakos Komvopoulos
13a TYPE OF REPCRT 13 TIME COVERED . 14 DATE OF REPORT (Year, Month Day) 15 PAGE COUNTFinal technical paper =ROM J 4 B TOj/61 30 May 1989 74
16. SUPPLEMENTARY NOTATION
17 COSATI CODES 18 SUBECT TERMS (Continue on reverse if necessary and identify by block number)
FIELD GROL10 SUB-GROUP
19. ABSTRACT (Continue on reverse if necessary and identify by block number)
The objective of the proposed research was to create hard layers on metallic surfacesin boundary-lubricated sliding and to investigate their tribological behavior. In addition,the goal was to investigate the basic mechanism of friction of lubricated metallic surfaces.
We have investigated the following aspects: (a) Experimental investigation of thetribological behavior of metallic and coated surfaces in boundary lubrication and (b) FiniteElement Analysis of friction and wear of the coated surfaces, and the delamination process atthe interface. '_o , - 2 3.
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00 FORM 1473,84 MAR 83 APR edition may be used until exhausted, SECURITY CLASSIFICATION OF THIS PAGF3 All other editions are obsolete
Unclassifed
FUNDAMENTAL MECHANISMS OF TRIBOLOGYAND THEIR IMPLICATIONS
Final Technical Report toThe Office of Naval Research
Contract No. N00014-82-K-0520
Nam P. SuhNannaji Saka
Kyriakos Komvopoulos
Tribology Research ProgramLaboratory for Manufacturing and Productivity
School of EngineeringMassachusetts Institute of Technology
Cambridge, MA 02139
May 1989
2
'ITable of Contents
I I. The Mechanisms of Friction in Boundary Lubrication .......... 4
I 1. Plowing Friction in Dry and Lubricated Sliding .............. 15
III. The Significance of Oxide Layers in Boundary Lubrication ... 28
3 IV. The Role of Hard Layers in Lubricated and Dry Sliding ..... 40
V. Wear of Boundary-lubricated Metal Surfaces ............. 49
II
Accesion For
NTIS C'IA&I
DTIC TAB 3Unannou ,cd :1
By
i Avibtfy Codes
D D is Av ,,o ,'l'd ior
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The Mechanism of Friction inK. Kamvopouios lI
m .oosM Boundary LubricationMer ASME
The primary friction mjechansm between boundary-lubricated sliding surfaces was
N. Saka nt estigated. Experiments were performed on well-polished aluminum. copper, andchromium using mineral oil lubricant. It was found that the prevailing boundarylubrication model, which is based on the adhesion between asperities and shearing
N. P. Sub of the lubricant film. cannot account for the formation of plowing groo'es on
polished surfaces. Scanning electron micrographs of the worn surfaces and surface
Degarrnent Of Mechanical Engineering proi/es hate shown that plowing is the dominant mechanism of friction inMassachusetts institute of Tecnnoiogy. boundary lubrication. Theoretical anal ysis has shown that the coefficient of friction
Cambrige. Massacnusetts 02139 depends on the sharpness and the sire of the entrapped wear debris or the surfaceasperities, and the interfacial "frictional" conditions. Reasonable agreement wasobtained bet ween theoretical and experimentalfriction coefficients.
I Introduction
More than sixty years ago, the phrase "Boundary properties of the lubricant film are the shear strength, meltingLubrication" was first introduced by Hardv. Hardy and point and good adhesion to the surface, and that film for-Doubleday [I) postulated that when metallic surfaces in mation may occur by physical or chemical adsorption. Therelative motion are separated by a thin lubricant film. friction %.arious factors (such as atmosphere. temperature, liquid-solidis reduced due to the physico-chemical interactions between interactions and chemical reactions) and their role in frictionthe sliding surfaces and the lubricant film. Consequently. the of boundary lubricated surfaces have also been reviewed b.early investigations on boundary lubrication were primarily Campbell 110).focused on such variables as molecular structure of the According to the prevailing boundary lubrication model.lubricant, environmental conditions, interfacial temperature, the friction force between boundary-lubricated surfaces is theand physisorption and chemisorption which govern the ad- weighted sum of the force necessary to shear the lubricantsorption of lubricants to solid surfaces. film. and that arising from the deformation of the surface
Beeck et al. (21 suggested that long-chain polar molecules, asperities at the solid-to-solid contacts. Thus. the coefficientwhen used to lubricate well-polished surfaces. form of friction. IA. is expressed as [3. 41monomolecular layers by physical adsorption on metallic s', ) (--l-1surfaces resulting in low friction. Bowden et al. (31 later -O ( - ( .- Oasl (I)reported that even on rough surfaces a molecular layer of P. P.soap provides effective lubrication. They emphasized that the where s, is the shear strength of the lubricant film, s, and p..first adsorbed monolayer was responsible for good are the shear strength and the hardness of the softer metallubrication, and that the lubricating properties depend on the respectively, and a is the proportion of the real contact areachemical nature of the metallic surfaces. Bowden and Tabor on which the lubricant adsorbs and separates the asperities.(41 reported the importance of the molecular structure of the Some basic limitations of the above boundary lubricationlubricant and the chain length on the friction force between molel are at once apparent. First, for a given set of lubricantsboundary-lubricated surfaces. The physical properties of the and materials, the magnitudes of st. s.. and p. may belubricant film such as the film strength. contact angle, flash obtained, but the magnitude of the parameter a is not know ntemperature, etc., were found to affect the friction force a priori and. therefore, the coefficient of friction cannot besignificantly 15.61. calculated directly from equation (I). Second. the boundary
Campbell and Thurber 171 conducted experiments on steel lubrication model predicts magnitudes for the coefficient ofsurfaces lubricated with straight-chain hydrocarbons and friction that frequently contradict the experimentally ob-observed that the environmental humidity plays a significant tained friction coefficients. For example. when a reachesrole in the mechanism of boundary lubrication. They values close to zero, according to equation (I). p - s.1.,p..hypothesized that the high friction coellicients obtained in a From the shcar strength-hardness relation'hip for metals, thehumid atmosphere were due to the weakly bonded and less coefficient of friction in the limiting case is approximatel.strongly oriented lubricant molecules on an adsorbed water equal to 0.16 which is lower than that measured in air as wellfilm. Godfrey 18. 9] stated that the important physical as in inert atmospheres and vacuum. In order to explain this
discrepancy. Rabinowicz IIl1 modified the ratio s./p,,
Contributed by the TribolOM Diviso fot publication n the Jova.4AL OF equation (I) by introducing the effect of the energy ofTaztiLmom. Marniscrip rsemged at ASME Headquaiters. *t lbef 7. 19a. adhesion. He stated that high friction coefficients may be
4521 Vol. 107, OCTOBER 1985 Transactions of the ASME
obtained when the ratio of the energ' of adhesion to the plowing friction mechanism arising from the abrativepenetration hardness is high Alithough this rnodificaaion ma% action of the *ear debris may be important in the frictioncoefficients, it cannot account for the formation of plowing predominant friction mechanism in boundar% lubricatedstesIn qaditin. the aentali cobtsieswhiffrnt force.g Tnlhe uOof this paer althieforesltsdni hmodes ofasperity interairtions in order to obitain the normaland tangential forces and hence the coefficient of friction If Experlmental Materiels and ProceduresU The normal load was oitained "y considering a hard coneindenting a softer surface while the tangential force was A. Materis ad Lubrieat. Three metals were chosenobtained by considering only the interfacial adhesion of flat for investigation: Pure aluminum (99-9994 percent). Oltgenasperitis in contact. Such a separation of the modes of Free High Conductivity (OFHC) copper (99.9994 percent).Ideformation at a single asperity contact is physically and electroplated chromium. The primary reason for thisunrealistic, choice was the large range in the hardness of the three metals
In the past. much effort was also directed at the first term Because the objective of ibis study is to investigate the fun-of equation 41). By definition, for well-lubricated surfaces a damenital friction mechanism when two lubricated metallicmust assume values close to units, and accor ding to equation surfaces are sliding on each other. a-relatively inert. addjtii.c-I(1). s a silp. The lowest reported coefficient of friction of free mineral oil was used. The mineral oil consists primariyboundary lubricated surfaces is about 0.04. Because the of naphthenic hydrocarbons and has the following physicalhardness. p,, can vary by orders of magnitude, a %alue for P, properties as specified by the supplier. The density at 298 K isfor soft and hard materials within this range could onl> be 0.89 2/cm'". and the flash point temperature is 455 K. Theproduced if s, is a function of the hydrostatic pressure. p. kinemiatic viscosity at 310 K is 74 cSt and at 372 K it is I I cStIndeed, Ofriscoe et al. 1121 slid glass spheres o~er glass plate :1 speel.v proearalinacooled with a number of lubricants and obser--ed that s. in-creases with pressure in a roughly proportional manner. (a) Aluminum. Disks (2.54 cm in diameter and ap-3 Later. Rabinowicz 1131 suggested that at low hydrostatic proximately the same thickness) and cylindrical slider pin%.pressures s. is independent of the pressure. but at high f0.635 cm in diameter with hemispherically shaped tips 0 SPYpressures. s, is proportional to the hydrostatic Pressure and cm in diameter) were used. After cutting and machining, thethe ratios/lp, has a value of 0.05. disk specimens were polished with 600-grit SiC abrasi'.e
Although the predictions of the first term of equation (Il paper. Then all the specimens were annealed at 673 K. in argonI appear to be in good agreement %ith the experimnental results, for an hour. The annealed specimens were polished *ith 0 3there is a conceptual defect. It was assumed that plastic gum a-alumina and 0.05 pmn y-alumina to obtain a mirrordeformation of the metal surface occur, because of ihe finish. Then the specimens werte cleaned witl warm water andnormal load, and that the friction force arises only from soap. rinsed with isopropyl alcohol and stored in a desiccatorshearing of the lubricant film. Such an argument is basicall% with Ca-SO, at room temperature. Scanning electronerroneous since the plastically deformed SUrlace should aiso micrographs obtained after polishing and rinsing the uria':e%contribute, together with the lubricant, to friction during did not show ony SiC or Al.,O, particles embedded on thesliding, surfaces (similar observations were also made for the copper
Athird limitation of the existing friction model is that 11 and chromium surfaces after polishing). The hardness beforecannot explain the transition of the surface topography.and annealing was found to be 294 MPA (30 kg/nmmZ) and afterthe vviation of the friction force with sliding distauice. .annealing and polishing with alumina it was 116 "Pa 119~
Numerous investigaltions have shown that the coefficient of kg, mm-).friction undergoes significant changes before a steady state is Wb Coppe. As in the case of aluminum meni..reached. Recent experimiental results have also shown that the copper disks (2.54 cm in diameter and 1.27 cm -. io andcoefficient of friction can assume different magiliudes when cylindrical pins (sliders) 10.635 cm in diamc: ,r withthe stationary and moving specimens ere reuersed 1141- In hemispherically shaped sips of the same diameter) were uw.dorder to explain the transitions ofifte fricton cW"ieu with for the experiments. After machining the disk specimens tramUse distance slid, Suh and Sin 1141 postulated that the coef- 2.-54 cm diameter cold-worked rods, they were polishedficitnt of frictioln is not s material property ba noit as depends succssivey wri' 240. 320, and 600-grit SiC abrasive paper i.)on the ontibution of Whr friction mechanisms. defor- obtaineasmoc- -urface. The polished disks and the pins weremion Of Surface NsOtie ift Vwft *y -W P1rties en- the anieleki 073 K in argont for an hour to obtain a f ulsIipped At Lhe interam andf ad aspwsues. aW adhattion. rwcysaliaels -.racture which was free of residual stresses'
They wmIUWa shag *he conailenom of these frKictin The bardneu. after machining, and polishing with Si(.mechanisms to shearalf frictioa force dope -d ow only on abrasive paper was found to be 1,363 MP& (139 k.'mm.the eldhig atrials bee .w on sh solfw sopagraplw andl after annsealing andpoiushing with 0.3 pm a-allumina and 0 W'she mvsroenta. gad tha die comtausao by as~riy lio -alumiaa it wa 510 MPa (52 kg/mm-I. The specimensdeforomon and plowinau be peaer thn that by with nuo fiis were cleaned with warm water and soap.
adhofts.and ritsd with isopropiyl alcohol. Finally, they were stored inhs is apparent, therefore, that in addition to or in in au f the a doiscemor wish Co.-SO, at room temperature to protect
iuhoa i Ia- the werises an 0i me of Jm s *= *qlqp th adsi of wate vapor.a boom the thf surfaces. -oe other flesbmmeaW acewer comnlsaly in boundary 1Abrm-im - hId. c Cbwmiom. Mik secimens (2.54 cm ia diaer and
a.wdiosofspliiima .h(orasperity) a a Prolorlin of real contac area
F s foma - seastress whore the lubricant separatesL-normal force 5, - Sheat retrph of lriatthe surfaces
00owdigli flmn 9 w angle between com and the
P, 0 1 .w a sroave width 0 - coeficien of friction
.~~~huugyOCTOBER 19NS. Vol.- 107214U3
5
Table I Experimental materials
Hardne, %lPa) Temperature of
Material Before After annealing (K)
annCA1ing anneahng
Aluminum (99 9994roi _4 = . 186= 16 6-3OFHC Copper (".999414) 1363 = 5 10* 21 8'3Chromium(125 am. electroplated e.S90 : .'84on AISI 1095 steel)
W..T . Table 2 Test conditions
Load 2N (204g)Angular speed 4.5 rad/sTangential speed 0.6 cm/s to 4.32 cm.'sSliding distance 0.03m to 10mTemperature 294 K
Teprtr Lubricant mineral oil'LOAD Relative humidity 22 to 30%
Environment laboratory air.uLMC_ STA_ GS 'density at 298 K. 0.89 g/cm3
*,ISCOStt4 at 310K. 4 cSt
viscosity at 32 K. I I cStpromlchN" flash point temperature 455 K
DISK on the strain ring and by a recorder which was balanced an.calibrated before each experiment. The continuously. re1 Ordcdtangential force was used to calculate the coefticient of
I4- E: aDEP friction for each experiment. For each material at lea!, :ourexperiments were conducted depending on the scatter in cheFIe.1 Plon-dllk experlmental setup. data. For calculating the standard deviation in the coetti.ientof friction, the experimental data were assumed to ioilci% a
approximately 1.27 cm thick) were cut from AISI 1095 5seel normal distribution.rods. Cylindrical pins (0.635 cm in diameter with The wear tracks were observed in a Scanning Electronhemispherically shaped tips of the same diameter) were Microscope (SEM). Because of very low wear rates in .heprepared after cutting and machining AISI 1095 rods of equal lubricated experiments, a profilometer was used to tra e :hediameter. After machining and cleaning, the steel specimens wear tracks normal to the sliding direction. For each exwere polished with abrasive cloth to obtain a smooth surface. pertment at least three profiles of the wear track at differentThen the steel specimens were electroplated with chromium, locations were used for estimating the wear volume of the Jikapproximately 125 Ian thick. After electroplating with specimens. The wear volume of each pin was estimated ba:euchromium, in order to obtain a mirror finish, the disk and pin on the diameter of the circular worn surface and the radtub otspecimens were polished with 320 and 600-grit SiC abrasive the hemispherical tips. For the calculation of the standardpaper and 0.3 p a-alumina. The hardness of the AISI 1095 deviation in the wear rates and wear coefficients. the cx-steel after machining was 3,501 MP& (357 kg/mm2 ) while the perimental values were assumed to follow again a normalhardness of the electroplated chromium on the steel specimens distribution. Energy Dispersive X-ray Analyzer was used towas 6,590 MPa (672 kg/mm'). All the specimens were cleaned check whether the AISI 1095 steel subsurface was exposedwith warn water and soap, rinsed with isopropyl alcohol and during the tests.stored in a desiccator with Ca2S0. at room temperature.
Table I shows the experimental materials with their hard- III Experimental Resultsnesses before and after annealing, and the annealing tem- The friction coefficients of aluminum, copper, andperatures. chromium sliding on themselves for both dry and lubricated
C. Appoelucs The pin-on-disk geometry was used to sliding conditions are shown in Fig. 2. In dry sliding theconduct the friction and wear experiments. The experimental coefficient of friction has initially a low value and graduall%apparatus is shown in Fig. I. The disk specimen was mounted increases until it reaches a maximum. Then it either drops orfirmly on a plate whikh was rotated at 4.5 rad's (43 remains constat. In the case of aluminum, the coefficient orevolutions/mn) and the pin was held stationary in a holder friction has a high initial value of 0.85 and after a slidingwhich was attached to a strain ring. A polymethylmelh distance of approximately 2 m it reaches a maximum value oiaicrylte container was attached to the rotating disk to provide 1.2. Then it decreases rapidly to a steady value of 0. 73. Unlikea reservoir for the lubricant during the lubricated tests. At the aluminum, copper shows a lower initial coefficient of frictionend of each experiment, the loose debris and mineral oil were of 0.3, but after a sliding distance of 3 m it reaches aremoved by cleaning with warm water and isopropyl alcohol. maximum of 0.96 without changing as the distance slid in-All the tested specimens were cleaned with acetone in an creases. Like copper. chromium has a coefficient of frictionultrasonic vibrating container for a few minutes and then initially about 0.3, but the maximum value is 0.77 which i%dried carefully before observing in the Scanning Electron reached after 2 m of sliding. Then it decreases gradually to aMicroscope. The experimental conditions are listed in Table steady state value of 0.6.2. Some dry experiments under the same conditions were also When the metallic surfaces are lubricated, the coefficient ofconducted for comparison, friction decreases substantially. Again, aluminum shows the
highest initial coefficient of friction, but the steady stateD. FricMtio m Wow Measurements. The tangential coefficients of friction for the three metals are almost the
force was measured continuously by the strain gages mounted same. Aluminum has an initial coefficient of friction equal to
464 /Vol. 107, OCTOBER 1965 Tranections of the ASME
6
-4 ar< Co ec'
00
Z 0 5 0 5 2 5 C ! Z 4
SL0NG4SANELi62Cefceto rcinvrassiigdsac o lmnm
ki- 't.
I,05 25 K 5 4,- Z
SLDN STANCE3il 2I *r, m at Vrcinvrsssiig Yitnefo lmnmcopper, ___________ and chromium sldngoteslvsTeflldsybl
C)
Fig. 3 Surface profi" of disk specimens for different slidingdistances (normal load a 2N. mineral oil lubuicantY. (a) aluminum, (b)copper, and (c) chromium.
0.15 and rapidly reaches a maximum ,alue of 0.45. After S mof sliding it reaches a steady state equal to 0.2. The coefficientof friction for copper assumes initially a magnitude equal to1A and rapidly increase to a value equal to 0.1IS. The steady
state value is about 0. 17. Chromium shows an initial coef-ficient of friction equal to 0.13; after 0.5 m it reaches amaximum equal to 0.4 and! then rapidly decreases to a steadysitate value, 0.15S.
With tbe exception of the initial coefficient of friction of SI aluminum (unlubricated). the initial coef ficient of friction forall the otlier cases lies between 0.1 and 0.3. This is in Pig.0)
agreement with recent experimental observations 1141. Pwg 4 Weow tracks of alu"mum suace: 4el dask and 0) PonSelected swuae profiles of lubricated disk specimens are OItbiltaw OIPefOfLef I revolutioni O.Ur*
shown in ig. 3. In the case of aluminum (Fig. 3. top row), thesurface profies of the wea tracks indicate that the roughnessincreasies until a steady state is reached and then it remains the profiles of the chromium disk specimens for selectedsame. When the steady-state roughness is reached, grooves lubricated experiments. The surface profiles of the c~hromiumI10-30 jim deep have been formed. The middle row of Fig. 3 wear tracks indicate that the surface topography changesshows some characteristic surface profiles of copper disk rather slowly with the sliding distance while the depth ot thespecimens. The surface profiles again clearl) show a drastic grooves remains below 2 jAm. A comparison of the surfacechange of the initial surface topography. As sliding continues, profiles shows that the groove depth and the width of the 'AearIdeeper grooves are formed until a steady state is reached. track decrease as the hardness of the material increases.However, in this case the depth of the plowing grooves The steady-state coefficients of friction with the calculatedremains below 4 ;an. In Fig. 3, the bottom row shows the wear rates and wear coefficients, together with their standard
3Journal of TrIbligy OCTOBER 1965, Vol 1071I4SS7
Table 3 Experimental reslts*Mi-ni Coefflam wear rate (Cut3 .Cm) Wev Coeffticient *
(now am1) Pin Ot Total Pin Disk TotalPur~ealuminum .3sW1R (1.2* 1 ) X to (3-4 * 22)X 10 44 3!:, ixh to- ±.~x0 (9.lO6)iO Ii~e.
Eletroplsad CI15tOJI0 (7.51O.2x io0- (6.5 *2.0 X to 10 16 6.? 2)" i0 0A'4O.) O 2662.0)X IO~~ i
Fig.~a I q t~s0 wfdMsillW()ds n b i
worn surfaces were obtained as a function of the distance slidAlthough extremiely smooth surfaces were used in the c%periments. plowing grooves were formed on the slidingsurfaces immediately. The number of the plowing groo'.eand the width of the wear tracks were found to increase wsit hthe distance slid until a steady state was reached. Figures .1-6show the worn surfaces of aluminum, copper and chromium Idisk and pin specimens, respectively, after one resolutionPlowing grooves have been formed on all the surfaces in-dicating that plowing takes place from the very beginning ofsliding. A comparison of the worn surfaces shown in Fig4-6, shows that the number of plowing grooves decreases asthe hardness of the material increases. Material adherence o~nthe surfaces can also be seen, especially in Figs. 4(a i and (61Some typical wear tracks after a large number of re, oluion%are shown in Figs. 7.9. In all case the surfaces hae beenplastically deformed and many plowing grooves has e beenformed on both surfaces. Figure 7 shows that the aluminumdisk and pin specimens suffered extensive surface damage and I
Pig 5 Waow ouk f app. msuacs: IQ disk and 0) pin flubicted numerous plowing grooves have been formed especially an*evti~i. a WSUIUAW the pin surface. Figure 8 shows, in contrast with aluminum.
thilt the copper surfaces have been less plastically deformed.but fine plowing grooves have been formed. It can be 'ern Uthat the ridges of some plowing grooves have been ruptured
deviations, are shown in Table 3. The results indicate that the and many microchips have been formed. Figure 9 shows themateal hadness affects significantly the wear rate of the plastically deformed surfaces of two chromium specimensexperimiental terials, while the effect of hardness on the Plowing grooves are noticeable on the disk specimen andcoefficienit of friction, although noticeable, is marginal, material adherence on the pin surface can be seen. Rupture ol IHowever, the general trend that hard materials have low ridges and formation of microchips can also be seen on thefriction and wear seems to be followed also in boundary disk surface similar to what was found on the copper Ju'.klubrication. The calculated wear rate and wear coefficient of surface (Fig.- 8(a)). A comparison of the worn surfaces showbnaluminum are higher by an order of magnitude approximately in Figs. 7-9 indicates that the number of relatively large athan those for copper and chromium. These results are in plowing grooves and the width of the wear track decrease a%.agrgemnt with the surface profiles of the wear tracks (Fig. 3). the hardness of the metal increases. This observation is
In order to observe how the topography of the wear track consistent with the estimated wear rates for the three metals
chanes during sliding, scanning electron micrographs of the (Table 3) and the surface profiles (Fig. 3).41 VOL 107, OCTOBER 1965 Transactons of the ASME
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3Journal of Tr~bokogy OCTOBER IM8, Vol. 074,S?
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Fig, 9 WOW tracks Of ChnomIum siaicaco: (a) dsk ind () pin(lubricated exp~meirfet 1.920 revlutions (54.40)).
For a conical asperity (Fig. 10(a)). the normal andtar.;ential forces acting on an elemental area, dA. respc,-
• ~timely, are mt
1 ar dL=pcosedA 12)
- -dF=psin~cos-fdA4.ssin-ydA (3)
_ where dA = secO r dr dy, and p and s are the normal pressureand the shear stress, respectively, acting on the elemental areaas the cone plows. Integration of equations (2) and .3) oterthe front half of the conical surface where contact o,:cursyields the total normal and tangential forces, respectinef,., a,,
SW.
where %' is the diameter of indentation. The coefficient of
(4). as
Fi 10 ) sd Rmdes of weer debs: (a) cons and (hI s - [tane+ ( 5 )sec9] vs
Plowing can also occur from fragmentation of the ridges For a spherical asperity (Fig. 10(b)) the normal andformed along the sides of the plowing grooves and from tangential forces acting on an infinitesimal area, d.4. :an N-material transferred and strongly adhered to the surfaces. In expressed asthis case, the transferred fragment can act as a hard abrasi e dL -p cosl dAIgrain and plow the surface from which it was transferred.
In order to calculate the coefficient of friction due to dFupsincos'ydA +ssin-ydA 191plowing, it is assumed that the entrapped wear particles are where dA - r2 smin d0 d'Y. and r is the radius of the sphereeither conical or spherical. The experimentally obtained Integrating the above two equations over the front half of theoefficients of friction are then compared with those obtained sphere where contact occurs, the total normal and tangentialfrom the conical and spherical models to estimate the con- forces can be expressed as
tribution of the plowing mechanism to the total friction force. WBowden et al. (1S1 were among the first who attempted to L a - (9)model the plowing mechanism in dry sliding. Assuming a Ispherical or a cylindrical shape for the hard asperity. they
obtained simple expressions for the plowing force. Bowdenes [ial fond that when a small hemispherical slider of stel slides Fstpr2 sin ' - ! - W
on unlubricated indium, plowing accounts for as much as 2
one-third of the total friction. Theoretical calculations for r (w) I
such simple shapes as cones, spheres and pyramids have also + Zr'jI - I - 1 1 J (101
been made by many investigators 16-18), and the ex- 1
perimental results agree fairly closely with the predictions of The coefficient of friction is obtained, by dividing equation
these models (171. (10) by equation (9), as
4N I Vol. 107, OCTOBER 1965 10 TransactIons of th ASME 5
Copy cvailable to DTIC d-c: not
permit fully legible reproducion
CE 36 04,.A.,.Iv.• : ff . I ,e * z i,- w £,.,,i n,&~
3B .050,
000- 00' 8
_ _ _ Fig. 12 Coefficient of friction for a spheritcal asperity as a function of
O 20 " t. o *, ,2 ! the ratio of groove width to diameter of spher for different boundary"frictontlOnal" i' ono Points rersnt experimental data obtained
from lubricated experimentll with aluminum, copper, and chromiumIF. 11 Coefficient of friction for a conical asperity as a function of &i'ding on themselvea.the angle * for different boundary "frictional" conditions. Pointsrepresent axperimental data obtained from lubricated aperiments withaluminum, copper, and chromium sliding on themselves Fgure II shows several friction cures obtaed from
equation (12) (conical asperity) as a function ot the angle ,Y
and for different interfacial "frictional" conditions. It can-be.+2 r (_r ( ) Ir ): : seen that the experimental points fall closer o the bottome
I ~ ~ , [=( ") sin -- ( friction curves. Figure 12 shows the friction curs obtained3 2 r 2r I from equation (13) (spherical asperity) as a function of theratio - 2r for different interfacial "frictional" condition-,
_ -(I isimilar to those for the conical asperit. i. The experimentalI points again fall closer to the bottom friction cures Botr
where w is the diameter of indentation, models clearly show that the experimental points fall loer oIt is reasonable to assume that the normal pressure p ', the lower curve (i.e., the s/s, = 0 cure). (The experimental
approximately equal to the hardness, p.. . of the material ,alues of 6 and w,2r were obtained from the surface profilesbeing plowed which is equal to 6s.., where s.. is the shear as shown in the Appendix.) A comparison betwein Figs IIstrength. Using this assumption, equations :, cnd (i1) maN and 12 showsthat inthecaseof large wear particles (i.e.. largebe rewritten as magnitudes of 6 or w/2r) the conical model is in better
2 ,agreement with the experimental results. This may be an- )sece (12) indication that large wear particles are rough and angular in6 s, contrast to small wear particles which may be smooth and
2 2r [() round and thus can be idealized as spheres. The most im(- sin ) - portant result of this analysis, however, is that the coetfiient
r w 2 2f of friction as predicted by the conical and spherical models i,I+ - iIi ( in good agreement with the experimental results. Table 4 ,i..,(13) the steady state %alues of 6 and w,'2r, obtained from
3( S. )Ilubricated experiments, the calculated friction coeffi ieni.Depending on the interfacial conditions the ratio sis,. can from equations (12) and (13) for s/s., = 0.1. which i, a
assume values between zero and unity. For "ideal" interfacial reasonable assumption for boundary lubricated surface,. andlubrication, the interfacial shear stress. s. is the shear strength the experimental coefficients of friction. The agreementof the lubricant film. sj. which is very small in comparison to between theoretical and experimental friction coefficients i,the metal shear strenuth, s,,. In this case, the ratio s/s, ap- reasonably good.proaches a value close to zero and equations (12) and (13) can The analysis performed above using conical and ,pher).Jlbe rewritten as models to estimate the coefficient of friction considers. the
2 transition of the surface topography and the size of the ^earIA - tanO (14) particles in addition to the shear strength of the solid iurlaje.
I • and the lubricant film. Both models give good estimates for2 (2r ) 2w the coefficient of friction and also explain semi-quantitatisels
jamr(w) [sin" ( )) - w)[1 - ( ) (15) (he variation of the friction coefficient Aith the size oi thewear particles and/or the surface roughr and the elft at
On the other hand, for dry sliding conditions, cold welding at the lubricant on the coefficient of fric hrough the inthe interface takes place and the interfacial shear stress, s. terfacial friction conditions (i.e., magnit.. !ss.).approaches the shear strength of the metal. s.... and the ratio It is well known that when a lubricant ntroduced at the
sis. has a value equal to one. The frictio curses obtained interface of two sliding surfaces, wear is reduced by orders atfrom equations (12) and (13) and for s/s... equal to 0 and I magnitude. Experimental results under dry sliding conditionsrepresent extreme values; in reality it assumes an intermediate verify the above statement. Indeed. it was found that the wearvalue, rates of aluminum and copper under dry conditions were both
3 Journal of Trlbology OCTOBER 1985, Vol. 10714S9
11
Table 4 heoretical and experimental coefficients of frlction*Theoretical coefficient of friction Experimental
coefficientMaterial Conical model Spherical model of
6 Coefficient of W 2' Coefficient of fito
(deg) friction Is. s., = 0 1) friction Isis. - 0. 1Pure aluminum 19±*2 0.23±=0.04 0.62±=0.05 0.31 =0.03 0 ZU U02OFHC Copper 11±12.5 0. 14 =0.04 0.3" ,0.O08 0.17±0.04 0 I'=0.02Electropiated 6±r0.7 0.082±0.02 0.23 ±0.02 0.11 i ±0.02 0. is ±0.01
chromium
*Steady state t.alues
Table 5 Parameters of surface topography and friction coefficients at steady stateExperimental
Material Groove depth 6w/2r coefficient of frictionlA'mi (degi
Dry experimentsPure aluminum 10-60 29 = 3i 0.83 t 0.05 0.73 ± 0.04OFHC Copper 5- 30 16 = 2 0.53 ± 0.06 0.96 = 0.02Electroplated 7 -1 0.23±T0.04 0.60±=0.03
chromiumLubricated experimentsPure aluminum 10-30) 19 ±2 0.62 = 0.05 0.20 ± 0.02OFHC Copper < 4 11 z 5 0 37±0.08 0.17 ±0.02Electroplated <2 6 =0 - 0.23 0.02 0. 15 =±0,01
chromium
of the order of 10 cm'3/cm while for chromium it %kas 10)cm' ,cm. and the wear coefficients for aluminum, copper and
z chromium were of the order of 10 , ' 10 :,and 10 '20u41o respectixely. It is clear that the above wear rate' and %%earU *Cocn.Cl coefficients are by one or two orders of magnitude higher
or1-3 than those of the lubricated experiments (Table 31. In ad-
0 cdiiion, profiles of surfaces slid without lubricant sho%4ed thatI- : the surface roughness was larger, at least by a factor of t~o.
compared to the roughness of the lubrtcated experiment,Table 5 lists the range of the groove depths. the steadi. Nise
161 0 - magnitudes of & asnd w/~r. and the steady state coeltlicteni', )'friction, for both dry and lubricated experiments. It is clear
00- --that lubrication of the sliding surfaces reduces the magnitude,20IIN DIT 5CE 0o 0 . wl2r. and sl5,,. resulting in low coefficients of friction
$at ~Figures I I and 12 also demonstrate the validit of these_____________________________remarks.
03,Eaonf1 I OFi.. Cow An interesting observation regarding the magnitude ol the-Z 9 oo'a friction coefficient can be made on the basis of Figs. I I andWo 0 kconi~oi a 12. The experimental results from the lubricated experimens
WV * fall close to the friction curve that corresponds to s, s1& - the curve for which adhesion at the interface vanishe. rhis
-9o- implies that the contribution of the first part of equations 1121~.. ~and (13) (i.e.. equations (14) and (15)) to the total friction
00 coefficient in lubricated sliding is in general more significantSLIDING DISTANCE. in than the contribution of the second part for all values of 6 and
Wb w/Zr. Equations (14) and (15) represent the friction arising_________________________from plowing of the subsurface. while the remaining second
Z~ ~ *£wu' cAM..'..M part of equations (12) and (13) represent that due to the in*20.4 *Sofnceli ter facial adhesion.
U COROC61 To investigate the contribution of the plowing mechanis.m41 L as a function of the distance slid, equations (14) and IS) Acre1A.I used to obtain estimates for the plowing friction coefficient
0] and were then compared with the experimental %alues. TheW - calculated plowing friction terms from the conical and
su spherical models and the experimental coefficient of friction610.1. are shown in Fig. 13. Figure 13(a) shows the calculated
plowing friction curves together with the experimental :ur'.c%00 5 t iS 0 25 obtained from lubricated experiments conducted on
SLIDING DISTANCE. m aluminum. Both the conical and spherical models sho%% thatIC1 the plowing mechanism is responsible for most of the friction
pigis apW~anaI nd ~euawdploingfritio cometnta force. Although initially the plowing mechanism contribute'.YUSU13 Rallai iotao &M aul rm~ated ritoftmlont only 20 percent to the total friction, in the steady state ap-aluinlvum on aomwlinium. (at osppor on omiter. and ic .hathm on proximately 90 percent of the total friction force is due to theObuemlin plowing mechanism. Figure 13(b) shows the frictson cur'~es
40 1IVol. 107, OCTOB6E R 1985 12 Transations otthis ASME
obtained from the conical and ~Phc,,,d1 model, together with and shear of the lubricant film at the solid-to-solidthe experimental triction curse obtained tram esperiments on contacts.copper. During the earl\ stage, the plowing term accounts for20 to 25 percent of the total friction force . \k hen a distance of Akolegetapproximately 20Gm is slid, the magnitude of the plcss Ing term Ac oweg nsreaches 80 to 95 percent of the total friction force. Figure This work was done under the sponsorship of the Office of13(c) shows the calculated plowing rrimton curses together Nasal Research, Contract N00014-82-K-0520. The personalwith the experimental curve for chromium. The spherical support of' Dr. A. W. Ruff and Dr. R. S. Miller is greatl,model shows that 50 to 80 percent ot the total friction is appreciated.responsible for the plowing action while the conical modelshows that the contribution of the plowing term to the totalfriction force is between .40 to 60 percent. Figure 13 clearly Referencesdemonstrates that for boundary lubricated surfaces plowing is IHardy. W. B.. and Doubleday. L.. "Boundary Lubrication-The Paraffinralways the governing friction mechanism while adhesion Series." Proc Roe Soc. A. Vol. 102, 1922. pp. 550-514between the asperities and shearing ot the lubricant film have 2 Beeck. 0., Givens. J. W.. and Smith, A. E.. "On ihe Mechanism ot
mino cotribtios. oundary Lubrication I The Action of Long-Chain Polar Compounds." Procmino cotriutins.Ro, Soc 4. Vol I"I. 19W0. pp. 90-102.Nevertheless, if plowing of the sliding -surfaces, vanishes. the I Bowdeni. F P.. Gregory, J. N.. and Tabor. D.. 'Lubrication of Metalplastically deformed Volume should be reduced substantially, Surfaces b) Fatty Acids." Mature. Vol. 156. 1945, pp 91-1i01resulting in a sery low coefficient of triction. C oating the 4 Bowdeni. F. P.. and Tabor. D.. The Friction and Lubrication of Solids.surfaces with very hard layers will prev~ent plowing resulting Clarendon Preis. Oxford. 18,p. 17-.2eFiinPre-im0Vaouin only elastic deformations. In thi-' case the fnritin coef- Lubricants at High Pressures." Traits. ASME. Vol. 167. 1945. pp 5 I-59ficient will be, JAI = s,(pl 1P. where s (pi indicates that s is a 6 Appeidoorn. J. K.. *'Physical Properties of Lubricants.' Chapter 8.function of the hydrostatic pressure Ar. L nder these conditions Boundari, Lubrication, An Approsltof World Literature. Ed% Ling. F F.
pcnbe reduced *close to00.05 [131. klaus. E E .and Fein. ft. S.. ASME. New York. 1969. pp 133-144can -Campbell. W E . andl Thurber. E. A.. "Studies in BoundarN Lut'ri,.a-
The analysis based on the conical or rpheric:al hapes of the (ion-If Influence of Adsorbed Moisture Films on Coefficient ." lsiai, Fr,,wear particles is a simplification ot the problem since the wear ton Between Lubricated Surfames. Trans. ASME. Vol -0. 1945. pp 401-408particles are not necessarilly o1 a simple geometrical shape. A Gosdfrey. D . -Boundar'y Lubriation." Proc /it Siqsjr -An Lutir ind
Furterthe eloityfiel ofthe ateialbein plwed I it ar. Houston. Texs,~ 1963. pp. 283- 306.arthrrl The assumptiield o n a the mairial pl w i 9 CGodfres. D . "Boundary Lubrication." Interdisciplinari -ipproach to
abtaiychosen. Teasmto thtte aerl ov Friction and Wear, NASA SP-ili. 19U. pp. 335-384around the plowing asperity in planes parallel to the sliding 10 Campbell. lil E., "Boundary Lubrication:" Chapter 6. Boundart,surface is not quite correct. Moreov~er, the stresses ai the 1. ufrication 4n 4ppratsai of Worid Literat ure, Eds Ling. F F . islaus. E E3surfaces of the cone and sphere are also arbitrarils assumed to aflO Fein. Rt S . ASME. New York. 1969. pp 8"- 11
I I Rabinowicz. E . Friction and Wear of.44aerials. John Vuries. %e- I or khave independent hydrostatic and tangential components. A 196 pp 29-31. 65-61. 1"1-219.more rigorous analysis based on a slip-line tield is required. I.' Briscoe. B J . Scrsstots. B.. and Willis, IF Rt.. "The Shear Strength msAlthough an improvement for the estimation oat the plowing thin Lubricant Films." Proc. Roy. Soc. A. Vol. 333. 19'3, pp N~- 1 4
fritio foce s dsirble th man cnclsio ofthi in Rat'nowicz E FitonEpcal Low Friction." Fiindan~i'niarfricion orceis esirble.themain:oncusin ofthisin- T'slto ot, Eds s.,As. N P., and Saks. N.. The MIT.Press. C~mrnnll Il1Al
sestigation will still remain the same. i e.. plowing is t he l9b0.' 3 351-364
predominant friction mechanism in boundar% lubrication. IS %uh. % P . And Sin. H.-C.. "The Genesis of Friction," 14.v. %,,, IrV.
while adhesion and shearing of the lubricant film are 19, 1. pp 91-114IS Bowden. F P . Moore. A. J. W.. and Tabor. D.. 'The Pioughinji and
secnday. dhesion of Sliding Metals.' J of Applied Physics. Vol i4. 1943. PP 50-4116 Goddard. J . and Wilman. H.. "A Theory of Friction and wear Juring
V Conclusions the Asbrasion of Metals." Wear. Vol. 5. 1962. pp. 114-13!I'Hisakado. T . "On the Mechanism of Contact between Solid Sutia~ev
The major conclusions of this investigation are as follows; aul JSVE. %'ol 13. No. 55. 1970, pp. 129-139I itt Tzusizoe. T . and Sakamoto. T., *'Friction in Scratching without Metal(1# The primary steady state friction mechanism in TraInsier.- Rull IS3E. Vol. 18. No. 115. 1975. pp, 65-72
boundary lubrication is plowing Shear of the lubricantfilm between the sliding surfaces and adhesion betweenthe asperities, although may occur, contribute less thanIplowing to the overall friction force. APPENDIX
(2) The friction model proposed in this paper for boundarylubrication accounts for the formation of plowing Calculation of 9 and w/2r From Surface Profilesgrooves. Both conical and spherical models show thaI The experimental values of 9 and w/2r in Figs. I I and I2I the coefficient of friction depends on the sharpness andthe size of the entrapped wear debris and the surfaceasperities, and the interfacial -"frictional" conditions.i.e.. 0. w/2, and sits., respectiv~ely Reasonably goodI agreement between theoretical and experimentalfriction coefficients was obtained.
(3) The hardness of the sliding surfaces affects the plowingfriction mechanism. It was found that soft materials.such as aluminum, suffered more plowing than hardmaterials (e.g.. chromium). In any case. the plowingcomponent contributes mostly to the total coefficient of
3 (4) Thefrci contribution of the plowing ffict ion mechanism to Calthe overall friction depends also on the magnitude ofthe interfacial adhesion (i.e.. the s/s.. ratio). Theanalysis has shown that for very low values of 9 and plowingLIw/2,' (i.e.. for flat asperities and small wifear particles) oitvthe friction force may arise primaril% from adhesion FiglfAt Apealm tneap.lngovefisbvaswmilandesphm
3Journal of Trlboogy 13 OTOBER 1965. Vol. 1071461
were obtained from the surface profiles. It was assumed that (which is a reasonable assumption for shallow grooves) asgroove formation resulted from the plow ing action ot conical shown in Fig. A I, then it can be assumed that groove for-or spherical wear particles and or surtace asperities. Figure mation resulted from plowing by spherical wear particles (orAI"shows schematically a plowing grooxe formed bs a conical surface asperitiesl. In this case the measured values of w and h
or a spherical wear particle, were used again to calculate the ratio wl2r as following IseeFor each groove, the width. w, and the depth. h. were Fig. All
measured by a profilometer and the magnitude of 0 was r =(rh)- .(w,2)Iobtained from the relation r r-h:"-(w')or
8=tan L(2h/w) (A.1) w2
2r=h+ -Using equation (A. 1) se% eral values of 0 were calculated based 4
on measurements taken from at least four profiles of the same orwear track, but at different locations and al%,a.s normal to w 2h w]the direction of sliding. The values ot t so calculated were - =2 -+- (A.2)assumed to follow a normal distribution, and a mean %alue 2r INZhand the standard deviation for 6 were obtained. It ,as also Lsing equation (A.2) and following the same procedure asassumed that 0 was the same both in the direotion ot %liding for the calculation of 8, a mean value and a standardand in the transverse direction. Thus, the mean salue ot t), as desiation for w, 2r were obtained for each experiment andobtained from several profiles of the same xear track, and the assumed to be the same both in the direction of sliding and incorresponding coefficient of friction recorded just before the the transverse direction. The experimental points in Fig. 12
experiment was interrupted, were used to plot the ex- were then plotted based on the obtained mean values of w 2rperimental data in Fig. II. and the recorded coefficient of friction before sliding ,as
If the shape of the grooxe section is approximated b. an arc interrupted.
UIIIIII
III
4621 Vol. 107, OCTOBER 1985 Transactions of the ASME
14
IIII
Plowing Friction in Dry andK. Komvopoulos Lubricated Metal Sliding
Experimental evidence for plowing under dry and lubricated sliding conditions is.N. Saka presented and analytical "expressions for the coefficient of friction due to plowingare obtained. The theoreticalfriction coefficient was found to be a function of the
N. P. Suh sharpness of the hard asperities, the interfacial 'friction " conditions and the shapeof the plastic zone. The agreement between theoretical and experimental friction
Deoariment of Mechanical Engineering. coefficients from lubricated sliding and cutting experiments was remarkably good.Massachusetts Institute of Technology The discrepancy between theory and expe. iment in the case of dry sliding between
Camorioge. Mass 02139 like metals was shown to be due to plastic deformation of the asperities. Con-sequently, a different model for plowing was proposed for the case of dry slidingbetween like metals which produced estimates for the coefficient of friction in fairagreement with the experimental results.
I Introduction
In recent years it has become increasingly clear that plowing shearing does not occur at the original interface but that itby hard asperities and wear debris plays a predominant role in actually takes place in a direction slightly inclined to thesliding friction. Numerous investigations have shown that the surfaces 17). The observed mode of shearing in his ex-coefficient of friction is not a material property, and that it periments was primarily a continuous extrusion process,depends on parameters such as the surface roughness, the size somewhat similar to the process of chip formation in theof the wear debris and the environmental conditions. For machining of ductile metals. Antler [81 also observedexample, Suh and Sin 1Il in their interpretation of the separation of the sliding surfaces due to wear debrisvariation of the magnitude of the coefficient of friction with agglomeration at the interface. Hardness measurementsthe distance slid proposed that the friction coefficient must be indicated that the formed wedges were significantly harderexpressed as the sum of three components: asperity defor- than the metal surfaces from which they were formed. Hemation, plowing by wear particles entrapped between the suggested an analogy between the plowing action of thesliding surfaces or by hard asperities, and adhesion. In the agglomerated work-hardened wear debris at the interface andsame investigation it was also shown that the contribution of the built-up edge in metal cutting.plowing to the overall friction force in dry sliding cotild be A good deal of effort has been devoted in the past to derivegreater than that due to adhesion. Furthermore, recent work analytical expressions for the friction coefficient due toin boundary lubrication has shown that plowing is the plowing. The shape of the wear particles and the asperitiesprevailing mechanism of friction, while adhesion between the were approximated as spheres, cones, pyramids, etc., andasperities and shearing of the lubricant film have secondary expressions for the plowing component of friction were
effects (2]. obtained. Bowden et al. (9) in one of their early studies onThe significance of the wear debris in friction was pointed friction obtained simple expressions for the plowing friction
out long ago by Cocks, who performed experiments with force for spherical and cylindrical hard sliders of steel slidingcopper riders sliding slowly on drums made of copper and on a soft surface like indium. Goddard and Wilman 1101 laterindium 13-51. He observed that soon after sliding starts wear showed for spherical particles that the plowing friction term isdebris agglomerates and forms large wear particles (wedges) a function of the groove width to particle diameter ratio andbetween the contacting surfaces and separates the surfaces. that the coefficient of friction can assume values between zeroCocks suggesed that some sort of plowing action plays an and one. Hisakado 111) has shown that theoretical predictionsimportant role in the sliding friction, and that a based on conical, spherical and pyramidal models for thereexamination of the idealized cold welding between the wear debris were in fair agreement with those obtained fromasperities and the elastic-plastic deformation of the junctions abrasion experiments. Recently, Sub et al. (121 expiAed thewas necessary. Later, he observed that wear particle variation of the coefficient of friction with grit diameter inagglomeration, wedge formation and surface separation abrasion using a cone with hemispherical tip for the abrasiveoccurred also with flat metallic surfaces of different hard- particles. Based on this model, they explained semi.nesses (6). Cocks postulated that when sliding begins, quantitatively the transition from cutting to sliding mode in
abrasion.Although such analyses yield good estimates for the
Cont'ibiried by the Tribol Division of Ties AUwZastic .MlTY Of plowing coefficient of friction, they make use of ratherMCnACM. Euoumtum an preueud at the ASME/ASLE Tribolo Con- simplistic assumptions. For ample, the assumption that the
ren. Agdmst. Go.. Ocober 1-10, 115. Mafnuscipt re,,ed by th material being plowed flows around the abrasive particles inTholiogy Divism. April 29. 19 5. PAW No. IS-Trb-2. planes parallel to the surface leaving behind grooves of the
Journal of Tdbology JULY 12W, Vol. 10 120115
Table I Expermental resultsDry Experiments Lubncated Experiments U
Coefficient of Groove depth Coefficient of Groove depthHardness Friction (rm) Friction (;n)
Material (MPa) (steady state) (steady state)
Pure Aluminum 186.* 16. 0.73*0.04 o-6 0.20*0.02 5-20OFHC Copper 510* 2 1b 0.%*0.02 5-35 0.3 7*0.02 1-2Pure Titamium 3026* 131 0.48*0.02 1-6 0.46*0.01 0.5-4AIS I 1095 Steel 3500*451 0.50*0.08 0.5-4 0.12*0.004 <0.5Chromium 6590*284 0.58* 0.03 1-2 0.15*0.01 < Ielectroplatedon AISI 1095steel)
Annealed at 673 K for I hr in argon.Annealed at 873 K for I hr in argon.
same cross section may be correct in the abrasion of very soft DRY LUBRICATEDmetals (e.g., indium and lead), but in general it is unrealistic.Experimental results show that the plowed metal does notnecessarily flow in parallel planes, but that it deforms in amore complicated way resulting in ridges and wear debrisformation. Further, it was also assumed that the reaction ,I- / opmstresses at the interface of the hard abrasive and the metal loo, N'
being plowed are a normal pressure and a shear stress, and lthat they are constant everywhere. Although equilibrium is ( i
satisfied at the interface, the assumed stresses may not satisfyequilibrium at each location within the deforming soft metalahead of the abrasive particle. Moreover, it is not certainwhether the stress components satisfy the yield criterion in the Iplastically deformed region. It is apparent, therefore, that an 10 SON 100I0analysis which accounts for the shape of the plastic zoneahead and below the hard abrasive, and the correct state ofstresses and boundary conditions, may provide a bettersolution. Such an analysis can be performed using the slip-linefield theory t13-151. 1',
Gree 116) was the first to analyze the plastic deformation zro. 2o-.of asperity junctions in dry sliding under combined normal WI land shear stresses using the slip-line field theory. He estimatedthe forces for both strong and weak junctions using simpleshapes for the junctions. However, Green's analysis is ap-propriate only for obtaining the friction component due todeformation of the asperities. A different slip-line geometry is -necessary for plowing. 100pm W 2U Im
The different regimes of friction have also been studied byChallen and Oxley (171 who proposed three models using the I I loo,slip-line field theory. The first model, "rubbing model," wasbased on a slip-line field similar to that proposed by Green Mom .m
(161 for weak junctions and Rowe and Wetton for metalgrinding (18). The "rubbing model" is appropriate for F l P olies of disk speid... .fs f.om dry (M..et column) ad
lutdetM seond olumm) pkn-lk epedmenta with motals aNd onpredicting the friction component due to asperity defor- "Mlmelm e l low - 2N. mi .oa OuauieLat, in seir. 4a)maio, for it assume tht no wear takes place. The second aluinum (3o m. p) emepw (40.7 ). () titanium (U mft (4 A ISI0modal, "wear model," assumes that wear particles can be teel (M W iau kolumhm (JS. (4 alinum (W . m) oeppr1formed by plastic deformation and fracture of the softer (3161 ft ) itilum OLT7 ft V) AMS IM a"a (73. ml and (0asperie, but the proposed sip-line field does not satisfy the c (S. " .(Nlier in Pantfsee indlog theo l I
kinematc constraints on the problem. The third model."cutta neol," predicts friction coefficients and wear rateshibihr ha the previous two models. The proposed slip-line the chanSe in direction of a plastically deforming element offildd is oilr to that proposed by Lee and Shaffer 1191 for the workpce is assumed to take place abruptly after crossingm*MIWHowsm. ,the assuniedip-Une is mrmlstkc the shear phum. Moreve, the slip-line network does not
P, -bolatr forme shear angle in Henky's equations
F,m vatical force 6a,, = semi-asperity anglso/ - r@1do Of itefaclal shear strength to shear 6 - angle in hodograph
aotr b of deformed soft surface t1. la.j,. o,. 9, - "friction" anglesk~h5 kt, sher 0.0ths , anles in dip-line field
dm- sh strth (hardness) ratio of soft ,- coefficient of frictionsalfan to hard asperity u,te,u 1ot - principal strum
P .. - normal stress
i a Ifara d trnt - tangmtal stres~WI/¥oL 1M1,AY 618 TranVISCUoM of the ASUE
II
I
Fig. 2 Wear tracks Of aluminum surlaces: (a) disk and 1b) pin (dryexperiment in air, normal load = 2N. sliding distance 30 om)
account for the plastically deformed material sufficientlyahead of the shear plane.
Recently, Abebe and Appi [201 have proposed a slip-linefield for metal cutting with negative rake angles. Theproposed deformation field assumes chip formation andbuilt-up-edge at the nose of the cutting tool and it representsfairly well that observed in cutting. It was found that the ratioof the horizontal to vertical cutting forces decreases as the
rake angle becomes more negative, and that the ratio of the . -
chip thickness to the depth of cut is always greater than one. " .The proposed slip-line model can be extended to plowing .friction problems, for it accounts for wedge formation due to
material transfer from the plowed surface, and the formationof a ridge ahead of the plowing hard asperity due to materialpile-up. Furthermore, shear of the plastically deformed metalis assumed to occur within a shear zone and not simply along ,. lit.
a shear plane as in the previous models (17].The purpose of the present study is to obtain an analytical . , ,I solution for the plowing friction coefficient based on a model "
that represents fairly well the plowing process. The depen- . , •!dence of the friction coefficient on such important parameters " "as the sharpness of the asperities, the shape of the plastic zoneand the interfacial "friction" conditions is also examined. In lr
addition, experimental evidence for plowing in both dry and Fig. 2 wea tracis of copper w Maces 4s) disk and *) pin dry ex-lubricated sliding is presented and the range of application of perIment in air, noma load a 2N. sliding distenue - 30 m)
the theoretical model is discussed, experiments are shown in Fig. 1. In the case of dry sliding
(Fig. I. first column) grooves 10-60 pan deep were formed on
2 Experimental Evidence for Plowing In Dry and aluminum, 5-35 pm on copper, 1-6 imn on titanium, 0.5-4jpmLubricated Sliding on steel and 1-2 $an on chromium. The profiles of the wear
tracks of the lubricated experiments (Fig. 1. second column)Dry and lubricated experiments conducted on pure show that lubrication reduces the depth and width of the
aluminum, OFHC copper, pure titanium. AISI 1095 steel and plowing grooves significantly. The groove depth forchromium have shown that plowing grooves form on the lubricated aluminum was in the range 5-20 pm while thesurfaces. The experimental apparatus, which was a pin-on- grooves formed on the other metals were less deep. In par-disk tester, the methods of preparing the samples and the ticular, the depth of the grooves formed on copper was 1-2experimental conditions and procedures have been described pam, on titanium it was 0.5-4 pm and on steel and chromium itin detail in a previous publication 121. Although the specimens was less than 0.5 and I jm, respectively. In addition, thewere polished to mirror-like finish, grooves have formed on width of the wear tracks is much smaller in the lubricatedthe sliding surfaces at the very beginning of sliding. As sliding experiments than in the dry experiments. The effect of thecontinued, more wear debris and deeper plowing grooves have material hardmss on the surface topography and the coef-appeared. Surface profiles and scanning electron micrographs ficient of friction is also noticeable. The surface roughnessderly showed the transitions of the surface topography, and the friction coefficients were significantly smaller underespecily in the early stages of sliding. In both dry and lubricated sliding conditions except in the case of titaniumlubricated experiments the surface profiles indicated that the where lubrication was not effective. The general trend forroughness and the width of the wear tracks increase with lower friction coefficients when hard materials are slid on
sliding distance until a steady-state is reached. The grooves themselves is evidently followed. The hardness of the testedformed in the dry experiments were always deeper and wider metals, the steady state coefficient of fr'ction and the range ofthan those of the lubricated experiments, the groove depths are listed in Table 1.
Selected profiles of worn surfaces from dry and lubricated The transition of the surface topography was also studied
journl llO Trleegy 17 JULY 196, Vol. 106 13
- I
Flo. 4 Wear trackst of (an) urlos o diskt and (b) Pin(kItts~ltd exp~Wlnwo (mmllm ol1X normal loadl - 2N, sliding distar"o
periments. As in the dry experiments. the surfaces haviplastically deformed and many grooves have formed.However. the width of the wear tracks and the plowinggrooves are substantially smaller than those of the dry ex-periments. This reduction is especially noticeable for
~aluminum and copper wear tracks (Figs. 2-5).
These experimental observations clearly demonstrate thesignificance of the plowing friction mechanism in both dryand lubricated sliding. The variation of the surfacetopography and the formation of wear grooves during sliding
~can be primarily associated with the plowing action of wear
.1
debris entrapped between the sliding surfaces or with plowing
B H3 Analysis and Discussion
3.1 The Asslytlel Model. When a hard asperity, or ahard wear paticle entrapped at the interface, slides on a1softer eureacen plastic deformation of the soft material odcitn
due to plowing or microcutting. A material element ahead ofthe hard asperity is ntdefored but as it approaches theplowing paile extensive shearing and microchip formationoccur. The sheared material may produce a new wear particleor it my adhere strongly to the surface of the hard asperityresulting in the formation of rgid st nant region (deadzone) in front of the plowing ede in accord wi the ex-primntal evidence reported by Cocks o3-71 and Antler IS.
lop The similarity between sliding and maghiding as been
dc maed in asociat e wit the ploin ctne s of formationFi. I Weowtel of seer I i) dis and 0i) Pin 0 of a built-up edgje and a frontal bulge (or prow) in mindeqmpllemown6 al OW mel lo" a aI, didg distae .-m 4 dindint or cutting could be extended to the slidin problem
where ateal transferred and strongly adhered to thesurce asperities may s t as a -up edge deforming
with a scannif electron microcope. Several microglraphs of plastically the sufaces &M resulting in ridgle and wear debristhe mw tr3cks as a function of the distance slid were ob- formation. Rowe and Wetton D1tu. in their aoalyni for metal
three of the teted metals ane shown in Fig3s. 2-6. The A a and sug Mted that the pap haed asp-line model, which'ino of worn aluminum &d copper surfaces from acrunts for the formaeti of a frontal bulge shad of the
dry e&peiments mue shown in Figs. 2 and 3. respectively. It abrasive grit, could be assumed for modeling material pile-upcan be m that plastic deformation took plce as a resst of in front of the pi asperities in ft nS. Epermts_and tht many plowing grooves have formed on all of conducted with diuond cones t bravered on capper inated
the surfaces. Figues 4-6 show some typical wear tracks on that as sdinh proceeded mateial removed from the ploeing
discuVse. 10i, JULY 19ps6 18 Texamt oes of fMatnE
P~. W abe epw uress() ad) h ~ ofabultu eg ad rotl ule(o ro) nmeae~amnt~buei ei nmelWad* SNSiiA~ IUW U 4 U) gindig o cutin cold e etendd t th sldin prble
I
III
a
3 Fig. 6 Wear tracks of chromium surfaces: (a) disk and (h) pin(lubricated experiment (mineral oil), normal load , 2N. sliding distance
16m)
A r ~I
F
u£, 0 o -0 ... .......
F. 7 Plastic deformation due to plowing by a hard asperity (or wear C
grooves was eventually piled up and a prow, termed ridge,was formed ahead of the diamond rider (211. It is essential,therefore, that a slip-line field which may account for thisexperimental evidence must be used for analyzing the plowing
friction mechanism. fA slip-line field with these features is shown in Fig. 7. The U1
proposed field is similar to the one given for metal cuttingwith negative rake angle tools 1201; however the solution of U. U"
the present study is based on different assumptions. Inreference (20], it was proposed that the shear stress is a b)function of the real area of contact and the normal stress due Fi. s is) SlplIne field for plowing end 0) velocity diagramto the high normal pressures. In the present study, no such 010d111a160constraints for the stresses have been imposed, but it isassumed that the ratio of the interfacial shear stress to theshear strength of the plastically deformed metal is only a field shown in Fig. 8(b) is kinematically admissible. In orderfunction of the interfacial friction conditions. Moreover, the for a microchip (or wear particle) to form it is assumed that avalidty of the proposed slip-line field in terms of the semi- ridge HI and a dead zone BJC are formed. The material beingincluded angle a and the friction angles I (see Fig. 7) have plowed flows over the hard particle along the boundaries CJ,bm discussed. JR. and BA.
Figure 7 shows a stationary hard asperity (or a wear par- The slip-line field shown in Figs. 7 and 8(a) is composed oftide) and a softer surface moving with a velocity U. It also domains with orthogonal a- and P-shear lines. The triangularshows two families of slip-lines, denoted as a-lines and 5- fields AIl, HIG, and JDC, and the rectangular field IFEJ arelines, along which the shear stress is equal to the shear networks of straight a- and 0-lines. Because the a- and $-linesstrength of the material. A stagnant region, or dead zone. is have no curvature, the hydrostatic pressure remains the sameshown by the area BJC ahead of the plowing edge. The slip- throughout these fields. The centered-fans (sectors) GIF. RIK.line analysis is developed on the assumption that the plane- and E.JD, are networks of straight and circular orthogonaltrain condition approximates the plowing situation well. slip-lines. In these fields the hydrostatic pressure is the same
Figure I shows the proposed slip-line field with the along a radia line, but changes from one radial line tocorresponding velocity diagram (hodograph). The velocity another. The normal and tangential tractions on boundaries
JouIal Of Trbology 19 JULY 1986, Vol. 1061306
IHI and 1A are zero because HI and 1A are stress-free surfaces.Thus the a- and 6.lines must meet these surfaces at 45 deg. BC"TA0 i+ii 2 T-\ + 3 d -
The domain KBJ is a set of orthogonal a- and 0-lines 2
contained within the curved boundaries BK and Bi which are -0-1, +,17, >0
arcs of circles with centers at I and 0 and radii ID and OB,respectively, and a straight line KJ. The a-lines in KBJ are orarcs of concentric circles with center at I and the $-lines arestraight lines passing through I (Fig. 7). Thus, the hydrostatic 04- *3 > (7)
pressure is constant along the straight $-fines, but it assumesdifferent values on each $-line due to the circular a-lines. The Because the velocity along the $-line HGFEDC must be
details of the geometrical construction of the field KBJ are constant, the following relations should be satisfied (Fig. 8(b))given in the Appendix. UNo - UDC:
The angles q,. q2, and V3 which the a- and 0-lines makewith the interface ABJC depend on the interfacial shear orstrength, s,, along each of these boundary segments. The .1angles w., are given by s 1n4 s+a-Ij - 2 _ sin(l +1 3 + -o- a)
or s, =kcos(21?,) sin (3)4- sinh, 3 U,,=-cos-l(s/) j-1.2,3 (1) or
where 1.2, and 3 represent the boundaries AB, BJ, and JC, I~ +j +9-a-sin' [v2sin(4 +a-il -Z2)sinn, (8)respectively.
3.2 Geometrical Constraints on the Slip-Line Field. The and
proposed slip-line field assumes that material is removed in UEF = UHG
the form of microchips. In order for the chip formation or
then parallel to the rigid boundary AB. For this plastic flow to sin(! +a- 71, -29
take place the angles HiM, BIN, and J1N must be nonzero, sin(b+a- - 7) 4)i.e., the following relations must be satisfied sin6 sin( 31sTn T
HfM= - -20+a-,it >0or 4Or +9-a
2-4+- 2 2;1I( 9 ) IB N+a- 71 >0 +t[an Q- Vsin+a- i -2)si +9a) J9)
or~~ ~~ I-v2snQ+ - -20)cos(II + 6 - a)
The lengths AD and 08 can be expressed in terms of thed a>111 (3) slip-line field angles and the length JC as
andI
JfN=O+it -a>O cos( 1+ osin(i - 2 ++0o r A S -= J - ( 1 0 )
(4dcos -I, sine sin (1, 12k +
Combining relations (2H4) the range for 0 can be obtained 2as a-Ill cosisin(q, -112 +9+A)
and (5) sin9 sin (Il -112 +
4
The propos dipline field also assumes the formation of a 3.3 CAefflimt of FrIclOm. If p is the hydrostatic
dead nose BJC. For a dead zone to form, two relations mum pressure on a slip-line and # the angle of rotation of an a-line 3be satisfied: the sum of all the anges at point J must be equal with the x-axis (shea angle), the equilibrium equations and
to 2v and the angle 114J must be nonzero. Hence the yield criterion can be ombined into the following two
2 6 (1 S \ .equations known as Henky's equations (13, 14)
2 -A + p+ 20 - constant (a-line)
or p-2k-constant (l-line)
T The pressure, p. along any slip-line can be obtained fromA i + q2 + q( - (6) the known boundary conditions and equations (12). The
stresses at each location are then found from Mohr's circle.and The hydrostatic pressure. p. along some a- and 0-lines and the
0S1Vol. 106, JULY INS 20 TAlW N tOM of #1W ASME
3 normal and tangential stresses o and a,, respectively, alongthe boundaries AB, BJ, and JC are given in the following. - 0 + 20+ 2o)cos(O+ A- 2k) + sin(O + -2a- 2'73) (18)
On the stress-free surfaces HI and IA the principal stresses
are. a, 0 all = - k all, = - 2k Sim ilarly, the vertical force F , is given byFrom Mohr's circle the normal and tangential stresses on theboundary AB are:
Alongthe =9l+sin2*iq) oA,8=kcos21I (13) F, = JCk
Along the O-line 18 and the a-line BK the hydrostatic sin 0-0- 0)
pressures respectively are: \ [Thntestessp'8=k P8K=k(l+2tP)
0Then the stresses along the boundary BJ can be obtained from - (1+ sin2712)sin (0 - 2a -Mohr's circle and the pressure pBA as
o =k(l +20,+sin2i 2) oas=kcos272 (14) 9cos(0- 2a)
The hydrostatic pressure along the a-lines IG. IF. and JD, + -(2- cos2*)cos (-2a-
respectively, is given by sin 8
p1O=k pF=k(l+ 20) pJD-k(l+2+2o) 2
From Mohr's circle and the known pressure p.D, the stresses (I 2620on the boundary JC can be obtained as + 0+2 6sn( a os( + A -2,-13)
oJc=k(l +20+2o+sin2n.3) oc= -kcos217, 3 (15)J (19)
The horizontal and vertical forces F, and F,. respectively, whereacting at the interface ABJC can be obtained by summation = -172 + O aalong the boundary. Thus
Thus, the coefficient of friction, j, = F, IF., due to plowingF, = F~ + F +Fc can be expressed as
= AB[o'.*cosa- o-4 sina]
+ OB [ IScos(1 2-n, +a- ) JolIsinw, * 2cosW, + bsinw3 - ,sinw 2 j-, 5cosSW4 +sinw,
3 £Jsifl(n. - ? +a -k)Idoli Jolt, cosw1 - ~iW 3OW 4OW1+isn4+CW
+ JCfo',Ccos(W- A - + 17i - 0+ where20
and + esin(v -A- 7 + 17, - + a)] (16) + I, ASsin(O + A - a) -2O .I
+ Ff + F ~F~~+ c t= it sine E2 -I+ sin2i 2
-ABleo Osina + vA'cosal sin (0-0- 2)
+ OBL H o: 'sin(12 - i + a -t ) 9 G 2- OS212 /s - I +20+2*
+ of€cos7 2 -j, +a-0) Id sn
+ KCt csin(r _A I, + q 2 - + a)
- fCls(1rA 1-- 9+I (1 7) (aI I1I-i- d2 02 -- +,-1- 2
where W1=4+I a W WO 22 w 0
Substituting equations (10), (11), and (13)-(15) into It is evident from equations (18) through (20) that theequations (16) and (17) and integating, the horizontal and coefficient of friction depends on the emi-uperity angle a,
erucal forces acting on the interface A C can d e obtained. the ratios slk (i.e., the "frictio" conditon at the interfaeThe horizontal force, F, is given by ABJC), and the magnitude of C. There can be an infinite
"number of solutions for the friction coeffi t within the
44 , s(;+ !)i~ 1 a iiss yrltos(S). The stres field in adeomnF, = j a4 materi can be uniquely defined only when the boundary
sn a-0sin#Godtos(tue or velocitie) of the deforming zone arei competelyspecified. Then the actual state of stresses. can be
0 obtained from the extremum principles propoes by Hill [221+ 01 +WIn2 )CO 0- 2a- for a rigid-plastic body. In machining problems, however.
some of the boundary conditions are unknown ad.3 .Os - 2a) 0) moreover,(the bo2)]aanthemacii~rc s lvswel u detemned.3 In+ 0-(2 - €os2qz)sin (0-2a- this cone, the ettremum principles am no longer applicablesi!2 and the machining process bs not uniquely defined t21. In the
2i present analysis, therefore, the angle 0 was varied within the
3 Jounal of Tdklmo y JULY I6, Vol. 1061107
09 1 1I
0 08
0?- %-/k-00
02 0,7 01.. 7Q2\' .2
2 \\\\ - o'Ug, o 06S0 0
~0- -. mUo N o-'I *- I
04 04r066
06 04
05- 0" 002 " 0
,,,.co\' j o.I. •09 45 50 55 0 65 70 75 80 85 90
,5 90: 99 60 653 ?0 ?9SQ 69t: 0 a (deg].) i
Fi p.llne1 fiel solutiOnl col oefflc~ent of i tl o 3I
limits set by the relations (5) and the minimum and maximum similar (or compatible) metals. in the limiting case for whichmagnitudes of the coefficient of friction we-re obtained as s/k- I, i.e., for "sticking" interacial conditions, the a- andfunctions of a and s sik. s-lines will meet the boundaries tangentially and at right
The minimum and maximum magnitudes of the coefficient angles. in this case the proposed slip-line field cannot exist. Uof friction as a function of the semi-asperity angle a are Nevertheless, "sticking' interfacial friction conditions areplotted in Pigs. 9(a) and 9(b), respectively, for the case when unlikely to prevail even with similar metals sliding onthe same "friction" conditions prevail along the interface themselves under dry sliding conditions, due to surfaceABJC. i.e., for it= -2 - ,. Several friction curves for dif- contamination which reduces the interfacial shear strength Uferent boundary "frictional" conditions s/k are shown. The and results in s/k magnitudes less than one.coefficient of friction obtains high values when a is low (sharp In order to examine the accuracy of the thereticallyasperities) and decreases rapidly to very small maqgnitudes for predicted coefficients of friction, experimental results from Ihigh values of a (shallow asperities). Moreover, the our study and other investigations were compared with Imagnitude of s/k affects the coefficient of friction theoretical solutions of similar s/k magnitudes. Hisakado 11lIIsignificantly only when the semi-usperity angle is surficiently slid conical diamond sliders on carbon steel and coppersmail. When a taka values in the rangde 45-55 deg., for (typical case of dissimilar pairs) and obtained values for Sik-•Iample, varitions of the magnitude of s/k may alter the between 0.1 and 0.12. Moreover, when carbon steel was slid
coeffitim of friction by S0 percent. Conversely, as a in- on itsef, a cse which my be interpreted as sldn betweenI€eege the effect of the interfacial friction on the magnitude similar metals, a value of 0.4 for s/k was deduced. Tsuki'oeof the coefficien of friction becomes margi~nal, and Sakamoto [2l, Z41 conduted siia experiments and
Th ofiin of friction predicted here is correct only reported a value for s/k equal to 0.11 for diamond concawhen the gueometri constraints given by equations (SH-9) aure sliders trvesig on copper, aluminum and low carbon Steed. Isatisfied. The dashed-curve in Figs. 9(e) and 9(b) is a limiting However, when sintered carbide conical sliders were traversedcurve for the assumed slip-line field. Outside this dashed- on copper the deduced value of s/k wats about 0.22. This cancurve different slip-lne fields must be sought. The friction be interpreted as a case of sliding between mterials of partial mcurves corresponding to low values of the ratio s/k masy be the or poor ompatibility. Friction data for conica diamond tolalppropriate curves for lubricated slding conditions, or for of different negative rake angles traversed on AIS! 1095 steelunlubricated sliding with dissimilar (ncompatible) metals have also been reported recendly by Sin et a. 125l. Figure 10_
" where tie interfaciad adhesion will be weak. Furthermore, the shows the minimum and maximum friction coelt icient curvesfriction curvesassociated with highvalues ofs/knmybe the for s/k -0.0, 0.1, and 0.2 together with obtained ex-.aporaecurves for unlubricated liding conditions with perimentad data. The experimental results shown in the figure
3MIVOI. 106, JULY 196622TranaaotlhlettlhSASlMt
22
II E : %y Table 2 Experimental and theoretical friction coefficients"-s s9'r a Coefficient of Friction
STANIUM (deg) Experimental' Theoretical (s/k = 0.7)' " $/k ' • LUMINUM%1 -CCE rain max
*CHROMIUM 45 0.50 0.54 0.55"k\ Q $G A s, .o95 ST[EE . 50 0.46 0.46 0.48,A11I 55 0.40 0.40 0.42
- TSUiJ(OcE a SAKAMIOTO 1 60 0.37 0.34 0.36
Iu I >.CZ :::IT a SUData*~ fro Reference 210.5 T
r I -F N
45 5C 55 60 65 7C '5 s0 65 so
a (deg.) Fig. 11 Slip-line field for plastically deforming hard asperity duringFig. 10 Theoretical and experimental friction coefflcints obtained plowingfrom lubricated (tilled symbols) and dry (open symbols) experiments
I with conical sliders [21, 24. 251 microcutting of the soft surface occurs. However. undercertain conditions plastic deformation of the hard asperity
have been obtained from lubricated experiments conducted may take place, despite the lower hardness of the opposedwith like metals sliding on themselves and from cutting de surface. Kayaba et al. (27, 281 have shown that when thequoted n references [21, 24. 25 . It is evident that the asperity angle is less than a critical value, which is determinedagreement between theoretical and experimental friction by the hardness ratio between the asperity and the flat sur-coefficients is remarkably good. In the case of the lubricated face, the hard asperity undergoes plastic deformation evenexperiments the calculation of the angle a was based on the though it is harder than the mating surface.obtained surface profiles. It was assumed that the formed Figure I I shows a possible slip-line field for a plasticallygrooves resulted from the plowing action of hard surface deforming hard asperity. The figure shows a hard asperityasperities (or accicular wear particles entrapped at the in- and a soft surface which have both deformed plastically at theterface) of the same semi-included angle cr. For each ex- same time. In order for the slip-line field shown in Fig. I I toperiment at least four profiles were obtained at different form, the angles BHC and GDF must be nonzero. These
locations of the wear track and perpendicular to the direction constraints yield the following relationsof sliding, and a mean value of a was calculated. The data of 31r-2af, - >0the lubricated experiments plotted in Fig. 10 are the mean 4values of several experiments obtained for different slidingdistncesorSatisfactory agreement was also obtained between ex- ,,> 3r (21)
perimental and theoretical friction coefficients for large 4values of s/k. Table 2 lists data from an experimental study andon machining of steel with carbide tools of different negativerake angles by Komanduri (26), and theoretical results ob- C+, - ->0
tained from the slip-line analysis for sit -0.7. The agreement 4between theory and experiment is indeed reasonably good. or
A comparison between theory and experimental resultsobtained from lubricated experiments between like metals and -,> - - a (22)
unlubricated experiments between similar and dissimilar 4metals, when the plowing surface was significantly harder where the subscripts h and s denote "hard" and "soft,"than the plastcafy deformed material, indicates that the respectively. The slip-line fields ABH and DFE are fields ofaccurcy of the theoretical model is remarkably ood. onstat pressure equal to, k, ad k,, respectively. Then theHowever, the agr'eement between theoretical Then, thHoeeteareetbtentertcladepressure in CDH and HDG can be obtained from Henky'sperimeutal friction coefficients obtained from unlubricated relations (i.e. equations (12)), and the nortand frotngentialexperiments with like metals sliding on themselves, appears to relaon ie itan () and th nor l nd t ebe Inadequate. This discrepancy between theory and normal and tangential stresses on HD calculated from the
is discussed next. slip-line fields of the hard and soft materials, ch.. 0A and al.
3.4 Valit of te Analytleal Modd. It has been shown
so far that when the relations (5) through (9) are satisfied, i = k (I - + 4 + 2, + sin2ih (U)solutions for the coefficient of friction in reasonably goodalreement with the experimental faults can be obtained. One 4- kO52q (23b)of the major assumptions of the analysis is that the hardasperity does not deform plastically when plowing and and
3 Jounlal 1 Tilogy JULY 106, Vol. 1061123
In the present study a assumes values in the range [i/4. Ie, = k,( I - .2 + 2a + 2%, + sit.1 (24a) ir/2]. For this range of values of c, the relation (29) and the
right hand side of relation (30) are always satisfied. The only= k,cos2, (24b) constraint to be satisfied then is
Along the interface HD equilibrium must be satisfied us. 31rif , = =s, from equations (23b) and (24b) it follows cos -(m) > - -4a (31)
2= cos-'(no (25) In conclusion, when a<a[, where a, is given by equation
(27), and relation (31) is satisfied the coefficient of friction Uand can be obtained from equation (28). Conversely, if a> a, the
I (6 hard asperity does not deform plastically and the coefficienti, = 2 COS (26) of friction is given by equation (20) if relations (5) through (9)
are satisfied.where m=k, /k is the shear strength ratio, which is equal to When the asperities are much harder than the plowedthe hardness ratio, and f=s/k, with 0 < m < i and 0 sf< I. surface it may be assumed that m < <0.1. For the particularKayaba et al. 1271 used a similar analysis and by equating the case that m 0 0. 1 equation (27) predicts cc = 20 deg for allnormal stresses oA and e. at the interface HD, they obtained a values of f between 0 and 0.9. This implies that only therelation for the critical value of a. denoted by a, in the asperities with semi-asperity angle less than 20 deg will Upresent work, as follows deform plastically. Because this value of a, is significantly
I____ ,f less than the values of a obtained from the dry and lubricatedcc ( m - 1 + -(3-) + mcos experiments, it is reasonable to assume that only the softsurface will undergo plastic deformation. In that case, the I
-Cos'(nuf' *fl II (mj)2 11 (27) coefficient of friction is given by equation (20) and the I- agreement with the experimental results is very good (Fig. 10
and Table 2).This equation gives the value of the critical semi-asperity For lubricated sliding conditions it may be assumed thatangle as a function of the hardness ratio m and the interfacial f=0.1, and for m between 0 and 0.8. for example, thefriction conditions f. For a given set of m and f, all the magnitudes of a, predicted by equation (27) were lower thanasperities with a < a, must deform plastically, the values of a obtained from the lubricated experiments.
In the presen ;tudy the above analysis has been extended Thus, under lubricated conditions a > c and equation (20) 3further to obtain a relation for the coefficient of friction when can be used again for estimating the coefficient of friction.plastic deformation of the hard asperity and the soft surface The agreement with the experimental results for this case istake place at the same time. Equations (23a) and (23b) can be also satisfactory as shown in Fig. 10. It remains, then, toused to calculate the vertical and tangential forces (see Fig. II) examine the disagreement between the theoretical coefficientsand hence the friction coefficient from the relation ju = F, IF.. of friction obtained from equation (20) and those obtainedThus from the unlubricated experiments with like metals sliding on
themselves.
[I - + 4a + cos '(m)cosa + sin(a + cos '(MAJ It is reasonable to assume that in dry sliding f varies be-2 I tween 0.2 (contaminated surfaces) to 0.9 (clean surfaces). If3r this range forf is considered, equation (27) may predict values
I- j +,4o+cos-'( j)Isina-cosla+Cos'(m)j of a, higher than the values of a obtained from the dry ex-L 2 periments. Thus. if relation (31) is satisfied the coefficient of
(28) friction must be obtained from equation (28). It was foundthat for m - 0.S, 0.9, and 1.0 and for f between 0.2 and 0.9,
Since Osf<l and O<m<l it follows that 0 mf<l. relation (31) is indeed satisfied when a assumes values equalTherefore, from relations (21). (22). (25). and (26) the to those obtained from the dry experiments and also thatfollowing relations must be satisfied in order for the assumed a< a,. Thus, for unlubricated sliding the theoretical frictionslip-line model (Fig. Ii) to be valid coefficients were obtained from equation (28). Table 3 lis
the values of a obtained from the dry experiments, the-a< _os-fc (29) orrmponding experimental frktion coeffikients and the
-a<(9)theoretical friction oefi obtained from equation (28)for m -0.. 0.9, ad 1.0. The table also lsts the values off forwhich solutions that satisfy the criterion a a, and the
3w I relation (31) were obtained. The agreement between theory-2a< cos- (Mf) S i (3) and experment is reasonable. It must be mentioned, however,
TAWS. 3 FApemeetal and tbeesrel e nmefid Of Is.11et fee dry 81001
Coeffdent Of FrictionEap moal Toetica (0.2 sfs 0.9)Jk~uer~a (de, (ezpurmts) , m-0.9 a.1.
Pwe lsmiawn 57* 15 0.73*0.04 0.73-1.46 0.75 - 1.46' 0.76- 1.40'
OFHCCOpper 71 *9 0.96*0.02 - 0.40-0.76 0.40-0.90PureTttanium 61 * 10 0.48*0.02 0.63 - 1.0' 0.64-1.36 0.65-1.33IAISI 10" Sed 64*9 0.50*0.08 0.35-0.73' 0.56-1.12 0.57- 1.411Electroplted 76*6 0.58*0.03 - 0.30-0.520 0.30-0.67
ChromiumOSoluctons valid for 0.2 s/sO.8 3bSutiom valid for 0.2 sfsO.7
'Solutions valid for 0.2 sISO.6
101VOIl. 10, JULY 19S Trmneca om of the NE 3124
that due tu the large scatter of -he magnitude of a. a direct good agreement with the friction coefficients obtained fromI comparison between theoretical 'r'tction coefficients based on lubricated and cutting experiments.the mean value of cr and experimental coefficients of friction 3. In the case of dry sliding between like metals, plasticmay not be appropriate. Consequently, the agreement be- deformation of the plowing asperities may take place. A slip-tween the predictions of equation (28) and experiments can be line model that accounts for plastic deformation of theimproved if solutions for the theoretical coefficients of asperity and the plowed surface at the same time wasfriction based on the statistical distribution of at are obtained proposed. The friction coefficients predicted by this modelfor each metal. However, this will require further analytical art. in fair agreement with the friction coefficients obtainedwork based on the topography statistics. Nevertheless, since from uniubricated experiments between like metals.te agreement between theory and experiment given in Table 3
is acceptable, such an analysis has not been attempted in this Acnweg ntstudy.Akoweg nt
In the present analysis it was assumed that the plane-strain This work was done under the sponsorship of the Office ofcondition approximates the plowing situation well and that Naval Research, Contract NOO0l4-82-K-0S20. The personalIthe soft material deforms plastically forming microchips support of Dr. A. W. Ruff and Dr. R. S. Miller is gratefullywithout work-hardening. The good agreement between ex- appreciated.perimental and theoretical results obtained from the presentedanalysis ensures that the estimation of the plowing friction ReferencesI ~ ~~~coefficient based on the obtained analytical expressions is Sh..P.anSn.HC.TeGeeiofFctn"w,,Vo69appropriate. u.NP.adSiH-."TeGnssoFrcin"WaV.69
Although the plane-strain assumption approximates 1981. pp. 91-114.well a efind tchnque e~g, FniteEleent 2 Kornvopoulos. K.. Saka. N., and Suh. N. P.. "The Mechanism of Fric.
plowing fairly wlarfndtcnqe(g.FiteEmnt ton in Boundary Lubricattion." ASME JOUI,ALi or T~aouxoc. Vol. 10'7. 19"5.3Analysis) may provide a more realistic solution. Adopting an pp. 452-462.appropriate Finite Element Mesh for plowing, solutions for 3 Cocks. M.. "Wear Debrs in The Contact betw-een Sliding Metals." Jour-the coefficient of friction and three-dimensional deformation nialof Appilied Physics, Vol. 29. 1958. pp. 1609-1610.
4 Cocks. M.. "tnlictactioii of Sliding Metal Surface. " Journal of Appliedfields for the material being plowed, can be obtained. Physic,. Vol. 33, No. 7.,1962. pp. 2152-2161.Moreover, geometrical constraints similar to those of the slip- 5Cocks. 4., " Frictional Interaction of Indium Surfaces. " Jouermal of Ap-
line analysis need not be imposed on the finite element plied Pftysic Vol. 36. 1965. pp. 649-650.analysis because the solution does not depend on an assumed 6 Cocks, M., "Role of Displaced Metal in the Sliding of Flat Metal Suar.
coeficiet offaces." Journal of Applied Physics. Vol. 35. No. 6. 1964, pp. t80'-1814flow field. This implies that solutions for the cofiin f 7'Cocks. M4.. "Shearing of Junctions Between Metal Surfaces." Wear. Vol.friction can be obtained for any interfacial "friction" con- 9, 1966. pp. 320-328.
ditions sfk, and any magnitudes of the semi-asperity angle or. 8 Antler. M. "Processesof Metal Transsfer and Wear." I~ea,. Vol. 7.,94
In aditonthe ffet o wok-hadenng f th susurace 9 Bowden, F. P., Moore, A. J. W., and Tabor. D., "The Ploughing andcan be included in a three-dimensional finite element analysis. Adhesion of Slidng Met.als." Jouial of Applied Physic. Vol. 14. 1943. pp
However, an analysis like this for plowing could be expensive W091and may not be necessary for determining the coefficient of 10 Goddard, J.. and Wilmaa. H.. "A Theory of Friction and Wear during
fricionin mst ase. Itcanbe ffecive in the Abrasion of Metals," Wear. Vol. 5, 1962, pp. 114-135.fritin n ostcaes I cn b efetiehowever, I II Hisakado. T., "On the Mhans oCntact between Solid Surfaces,"
predicting the wear coefficient in abrasion, where the problem Bulletin of the JSP4E, Vol. 13, No. 55, 19V0, pp. 129-139.is a contiiiuous chip formation and metal flow around the 12 Suh, N. P.. Sin, H.-C., and Saka, N.. "Fundamental Aspects of AbrasiveIhard abrasive (i.e., a three-dimensional problem). Wear." Fundamsentals of Triboloy. Ed&. Sub, N. P., and Saks, N., The MIT
and heortica reslts f thPpreent , Cambridge. MA. 1980. pp. 493-518.From the experimental an hoeia eut ftepeet 13 Hill, R.. 77e Methenwarnal Theoa'y of Plasicity. Oxford University Press.
study it is evident that plowing indeed plays an important role1 London. 1967, pp. 125-lO.in friction under both dry and lubricated sliding conditions. 14 Kachanov. L. M.. FAdasiamentib of the Thewi' of Pfasticity. MiltIThe magnitude of the friction force and the amount of publishers. Moscow. 1974. pp. 148-194.
1S Lee, E. H.. "The Theoretical Analysis of Metal-Forming Protilems inmaterial removal thus can be significantly reduced if plastic pln Stai. ASME Journal of Applied Mechanics. Vol. 19, 1952. ppdeformation and plowing of the sliding surfaces are made to 97-103.vanish. Deposition of hard and smooth layers (such as oxides, 16 Gres. A. P.. "Theg Plastic Yielding of Metal Junctions due to Comb iednitrides and carbides) of sufficient thickness on the surfaces Sh uW Prsur. Jou~, of the hiectomics en Phsc of Sohiils. Vol. 2.may result in only elastic deformation of the sliding surfaces. 17 Chjko. .~ M..an Oxley. P. L. B.. "An Explanation of the DifferentUnder these conditions the friction force arises primarily from Regimses of Friction ant; Wea Using Asperity Deformnation Models." woo'.s
interfacia adhesion and/or shearing of the lubricant film Vol. 53, I9M9 pp. 2296-243.I an, tuscoud bever lo. Frthemor, te war t Rowe, G. W., &bid Wetio. A. G.. "Theoretical Considerratins an theresistance of the surfaces could be increased by several ord r nin 1 fMtl,"J93.X0.eIasut o aus.Vl 7.1.Pof magnitude. Work in progress with metals covered with 19 La.E. H.. sA Shiaffer. 11. W.. "Thew Theory of Plasticity Applied to aoxide and nitride layers shows that indeed the deformation of Problii of Machining. " ASME iouunl of Apphsif Mchnsic. Vol. 18. 195 1.
the surfaces is primarily elastic and that wear is praictically PP. 40-.413.I 20 Atitte, M.. sad AM.I F. C.. "A Sligi.Litie Solutsion for Negative Rakeinsignificant.Aa& Cutg, Proc. Ninth N. Amser. Mllaiqlf. Am. Cisitf., SME. Dearborns.
MI. lost, pp. 341-548.21 Sakot, T.. sad Tmkaine, T.. "Friction ad Prow Forinaition in a
4 Com~udomg .~ ro of Coppe by a Diamio Caoe." Wow. Vol. 44, I9V7. pp
The following conclusions can be drawn from the present 22 HE, R.. "On this Stm of Sume in a P11iml-RigW Dody, at the Yieldstudy: Point." phill"W"in Ahazine. Vol. 42, MI.1 pp. 866475.
1. Experimental evidence from both dry and lubricated 23 1aiwbumt P.. "Is thst Machinin Pra Uniquely Definedli" Anisabi ofsding demonstrates the signiaticancie of the plowing the CIRP. Vol. 27, IM.8 pp. 1-4.
mechaism nfricion.24 Tsuksie, T.. ad Sakoamoo, T.. "Firid in scratching withous MeOamechanim in frction.Transfer." 11fb N of the JSME. Vol. 18No. ItIS. 1975. pp. 65-72.
2. Based on the slip-line field analysis a relationship 23 Sin, H., Saks. N.. ad Sub., N. P., "Alieadve wea Mochusm said thebetwee thle coefficient of friction due to plowing and the Grit Sine Effect." W.. Vol. 5S.1979. pp. 163-190.
s oftheaspeitis, te iteracia "fictin" on- 26 Konsaltti, R.. "Sjom Aspet of Machkining with Nquaive Rake TookSsharpness ofteaprteteitrail"rcin o- Simulaing (itkind inla. J. Mint. Tool Doe. So., Vol. It. 1971. ppdition and the shape of the plastic zone was obtaned. The 22-2)coefficients of friction predicted by this slip-line model are in 27 Kayabs, T.. Kato. K.. =id Hokkksgswn. K.. "Thametiesl Analysi of the
3Journel of T lbology 25 JULY 1986, Vol. 10811311
IPlastic ielding of a Hard Aspenty Sliding on a Soft Flat Surface.- Wear, vol$7. 1983. pp 151-161
25 Kayaba T . Hokkirngawa. K . and kalo. K . "Experimental Analysis ofthe Yield Cruenon for a Haid Asperiqt Sliding on a Soft Flat Surface. 14 ear,
Vol 96. 1964. pp 255-265.
APPENDIXi
Geo~retfcall Constraudoa of the Domain KBJ A- line T F
TLie construction of the field KBJ is shown in Fig. 12. Fromthe geometry shown in this figure, it is found that IJB =(r/2) - ' - (9/2) and, hence, the circle (Q) which passes from ,I and B is geometrically determined. Thus, the intersection K
between the circle (Q) and the line which passes from I and Rmakes an angle 0 with IB defines point J. Consequently, thebisector of BJ intersects circle (Q) at 0. The boundary BJ of "the slip-line field can be obtained by drawing a circle (S) withcenter at 0 and radius OB.
Two characteristic slip-lines in field KBJ are shown in Fig. (S)12. Line TP is a $-line and the curve PR. which is an arc of acircle centered at I with radius IP, is an a-line. The angle, W.that the a-lines meet the boundary BJ is not constant. Itassumes a value equal to rl: at B and J and a slightly higher F19. 12 OaonIetdcalconOtonlonotfledKBJvalue between. This implies that the interfacial shear stress, s,which is related to the nterfacial angle, w. through thefollowing relation This assumption is fairly correct because the arc BJ of circle
(S) is very close to that of circle (Q), i.e., the distance PP' iss= kcos(2,t) very small so that the approximation 1O = IBO or ,,w = i, is
is not constant along the boundary BJ. In order to simplify valid. Thus, equation (1) can be used for calculating the shear Ithe calculations it is reasonable to assume that w, - r72. stress ,in the boundary BJ."
DISCUSSION IF. E. Keanedy, Jr.' K. Kato'
The authors should be congratulated for producing a quite Several analytical results to estimate the friction force andcomplete plasticity analysis of plowing phenomena in sliding wear type with slip-line field theory were proposed in the past. icontacts. Their model agrees very well with experimental fric- some of which are listed by the authors.tion coefficients obtained in a variety of tests with conical The authors should be congratulated in trying, to give asliders under both lubricated and unlubricated conditions, more precise analysis for the plowing process. The'agreementThose results point out quite clearly the importance of plastic between the calculated and experimental values of the coeffi- i3deformation in plowing and the major contribution of plow- cient of friction seems very good. But the discusser would likeing to friction in many sliding contacts involving hard to suggest some points to be checked for better understanding:asperities. The application of the model to the authors' drysliding experiments involving like materials prompts several (I) The question of the wear type: Although the authors'
sins, eer.in il ar like thaterials prot s seve analysis is for the plowing process which should not generatequestions, however. In particular, I hope that the authors wear debris, Figs. 7 and S imply the formation of microchips.might clarify the following points: Were any microchips of wear debris observed in the sliding
i. How were the semi-asperity angles used in Table 3 deter- tests and, if so, how large were they on the average?mined for the cases of like materials in dry sliding? Were the (2) Observations by other researchers: What would be the
across-the-groove surface profiles of the disk specimens experimental evidence for the existence of dead zone in their(Figure 1) used, and if so, would those across-the-grove studies?
angles be indicative of the angles of plowing asperities on the (3) The question of the quantitative differences betweenpin specimens measured in the sliding direction? Was there authors' and other researchers' calculated values. Everyfaces (eg. Figures 2-6) that asperities with a as small as 60" its reliability and usefulness, quantitative comparisons bet-
were aetually present on the pins? ween theoretical values by different methods are necessary.2. Could third-body particles (wear debris) be responsible How large would the quantitative differences be between
for nuch of the plowing? Either loose debris or debris ac- calculated values of authors and Chaflen et al. (All forumilatoa on the leading edge of the pins (as a prow) could eample?
have attack anglas as large as those used in calculations for The discusser obtained good agreement between experimen.Table 3. Such debris could easily be work hardened to a hard- tal values and theoretical values calculated with the theory ofam reater than that of the material being plowed. Cthlle et &I. [A21. o
3. It appeals that the authors assumed that all plowingasperities, induding both the rigid asperity of Figure 7 and the Additioall Refereseesdefortmaing hard asperity of Figure i 1. were conical in shape. At Clailf. J. M.. ael Oakey. "As Explanaion of the Differsnia Rpein of
Would the resulting plastic flow around the cone really be ap- Friction d WW Uin Asperity Deformatics Models." W., Vol. S., 1979.proimatd by plane strain condition? p. 229-43.
A Kato, ., ad Hokkirglwa, K.. "Abraive Wear Disgram." Pro n egsof Eeaourib 85 Coq'w Iteiatoe'sE di Thboogar, Lyon. Francs. Sep. 9-12.
"-TT.ohou Uuveirty. Sendai, Japan; Curreenly at NASA Lewis R teaahMeant-of Ef1silooeriets. Dairtnmut Coileile, Heew... N.M. 0375S. Costa. Cke ,W Mho.
3121 VoI. 106, JULY 19066 Transectone of the ASME26I
II
Authors' Closure dium and lead, the amount of wear debris produced is smalland the deformed material is displaced along the sides of theWe wish to express our appreciation to Professors Kennedy groove. This type of wear, where very small amount of
and Kato for their generous comments on the paper and for material is removed, has been referred to in the past as plow-the critical questions. We hope that our response will help ing. Alternatively, when the amount of wear debris is signifi-clarify the points raised by the discussers. cant the material is removed as in metal grinding, i.e., in
discontinuous microchips. Under these conditions the type ofReply to Professor F. E. Kennedy wear is microcutting.The angles in Table 3 were determined from the surface pro- From the friction point of view, however, plowing is re-
iles obtained perpendicular to the sliding direction. We have ferred to as the friction mechanism responsible for the forma-assumed that groove formation resulted from the microcutting tion of grooves due to the entrapped wear particles or hardaction of the entrapped wear particles and/or hard asperities, asperities. Consequently, the plowing friction mechanismand that the angle a is the same in directions perpendicular should not be confused with the particular type of wear.and parallel to the sliding direction. It is possible that some of Numerous studies in the past have shown that wear debris andthe wear debris adhered initially to the surfaces and ag- microchips are generated when plowing friction conditionsglomerated to form wedges (prows), such as those reported in prevail at the interface. This was also found to be the case inreferences '3] through [8), before it became loose eventually, the present study. Wear debris formation was observed in allThe micrographs of the worn surfaces have indicated, experiments. Because the focus of this study was on friction,however, that in most cases long plowing grooves formed systematic characterization of the debris was not attempted.parallel to the sliding direction. This experimental evidence However, wear particles in the range 1-10 m were observedsuggests that plowing takes place primarily due to the wear and the calculated wear coefficients were in the range 10-' todebris entrapped at the interface. Because microscopic obser- 10-2.vation of the interface during sliding is not possible, and the Furthermore, the analysis based on the slip-line model oforientation of the wear particles trapped at the interface can- Figs. 7 and 8 does not depend on the formation of wear debrisnot be determined, it was decided to use the values of a from and microchips. The friction coefficient is determined onlythe transverse surface profiles. Different kinds of ex- from the deformation field defined by the boundaries HI, IA,periments, such as with wedges of known cutting angles a or ABJC, and HGFEDC, and thus it is appropriate for any plow-with abrasive papers where the slopes of the abrasive grits can ing conditions, independent of the kind of wear.be measured, are necessary. Nevertheless, a comparison of the It is difficult to identify the existence of a dead zone duringtheoretical values of the coefficient of friction with experimen- sliding because observation at the interface when plowing oc-tal values obtained from cutting experiments with conical curs is not possible. The existence of a dead zone, however,tools of known angles a has shown that the aggreement was has been observed in numerous plowing experiments in thevery good (see Fig. 10 and Table 2). past with cutting tools and in metal grinding. Because plowing
With respect to the question about the plane strain assump- in metal sliding is essentially similar to metal grinding ( 18], buttion for the plastic flow, plane strain conditions can be as- on a smaller scale, it is expected that a dead zone will alsosumed to prevail when the width of cut is much larger than the form in front of the plowing wear particles and asperities dur-depth of cut. The plane strain condition is an appropriate ing sliding.assumption when the rigid asperity (or wear particle) has the As regards to the quantitative agreement between theshape of a wedge. The flow is then confined to planes normal theoretical friction values, our approach to the problem was toto the edge of the wedge and the problem can be analyzed fair- consider primarily all the qualitative aspects in plowing fric-ly accurately with two-dimensional slip-line fields such as tion. The proposed models are in agreement with the ex-those shown in Figs. 7 and I 1. Moreover, the plane strain con- perimental evidence obtained for plowing conditions. In addi-dition is a reasonable approximation even when the wear tion, the remarkably good agreement between theoretical anddebris and the asperities are idealized with spheres or cones, experimental friction values of our work and other studies, in-for example, provided that the depth of penetration is dicates that the theoretical models are also quantitatively cor-significantly less than the width of the formed groove. This is rect. The qualitative differences between our model and thosetypically the case in metal sliding where the penetration depth most commonly used in the past are apparent from the detailsto groove width ratio is much less than one. In the present given in the paper. Because most of these models are in poorstudy the depth-to-width ratio assumed values less than 0.3 qualitative agreement with the experimental evidence, any cor-(for lubricated sliding it was below 0.2) and thus the plane relation between friction values calculated from those modelsstrain assumption for the plastic flow seems reasonable. and experimental results must be fortuitous.Because the theoretical friction coefficients obtained from the In particular, the qualitative limitations of the models pro-slip-line analysis were in good agreement with the experimen- posed by Challen and Oxley 117) have been addressed in the in-tal friction results the plane-strain assumption, we think, is troduction. Hence, a quantitative comparison between ourjustified, model and those of reference (171 is unrealistic. In reference
[A21, however, a comparison between experimental values and0l* to pofeor K. LNG theoretical values obtained from (17 was attempted.The term plowing has been reserved for the plastic flow of a Although an artificial correction factor was introduced to
soft surface when a loaded rigid asperity slides over it. From bridge the gap between the theoretical and experimental fric-the war point of view, the plastically deforming materia tion values of that study, the apeement is poor. In fact, it wasflows upwards and sideways of the microcutting edge resulting found that the experimental friction coefficient values werein the formation of wear debris (microchips) and ridges. higher than the theoretical friction coefficients by 30 to 70Under certain conditions, e.g., for very soft metals such as in- percent.
I3 ora 1Tlo y2 7 JULY 1986, Vol. 106 11
III
The Significance of Oxide Layers iin Boundary LubricationK. Komvopoulos
Mem. ASME Analytical and experimental studies were conducted on oxidized and nonoxidizedpure aluminum, OFIIC copper, and electroplated chromium to investigate the roleof surf ace oxide layers in boundary lubrication. The effects of the thickness of the 3
N. Saka oxide layers, the elastic moduli of the oxide and the metal, and the normal surfacetraction have been addressed. In addition, several possible failure mechanisms ofboth thin and thick oxide films have been proposed. The experimental results have
N. P. Suh shown that low coefficients of friction, about 0. 1 or less, and especially low wearcan be obtained in boundary-lubricated sliding if the metal surfaces are protected
Ospartennt of Mechanical Engineering, from plastic deformation by sufficiently thick oxide layers. Scanning electronMassachusetts Institute of Technology, microscopy has shown that when the oxide layers are not ruptured, the wear of the
Cambridge. Mass. 02139 surfaces is negligibly small. in this case, the oxide-oxide contacts deform primarily 3elastically and the predominant friction mechanism is the shear of the lubricant film.Based on this evidence, a theoretical modelforfricton was proposed and the agree-ment between theoretical and experimental coefficients of friction was reasonablygood. Disruption of the oxide layers during sliding, however, was found to result inplastic deformation and plowing of the surfaces.
I Introduction ISince the early 195s much attention was devoted to the was due to the breakdown of the oxide layer due to incompati-
effect of oxide films on the friction and wear of sliding sur- ble strains at the oxide-metal interface, as was also proposedfaces. Low friction and mild wear of unlubricated metallic by Whitehead [1) and Wilson [6, 71 for dry sliding. Exper- 3surfaces were attributed to the presence of thin oxide films iments of Hirst and Lancaster (141 with different metals andwhich prevented the formation of intermetallic welds [!-41. lubricants have shown that the rate of oxidation influ-The formation of the protective oxide films during sliding was enced remarkably the effectiveness of the oxide films in reduc-studied by the electrical contact resistance measurements [5- ing friction and wear. It was observed that oxide layers which7), and the high contact resistance was assumed to indicate formed slowly at room temperature yielded lower coefficientsshearing within an oxide layer which resulted in low friction of friction as opposed to oxides formed at high temperatures.16, 71. Rabinowicz (41 has proposed that low friction ca.- be The significance of dissolved oxygen in lubricated slidingobtained only when the oxide films are sufficiently thick, was studied by numerous investigators. For example, steel 3about 10 nm. Also, the wear of oxide-covered metal surfaces rollers lubricated with plain mineral oil showed that the sur-in dry sliding was investigated by Quinn et al. Il-101 and an faces with high oxygen concentration suffered minimum wearanalytical model for oxidational wear was proposed. (I5]. Experimental results have *also been reported for iron-
By contrast, the tribological behavior of oxidized metallic chromium (16, 171 and iron-silicon (11 alloys sliding in ox- 3surface under lubricateld sliding conditions has received only ygen of controlled partial pressure. Low friction was obtainedmodest aztentioo. Bowden and Young [Il] have observed when the sliding interface was completely covered by oxidethat lubrication of clean surfaces with long-chain fatty acids mixtures and oxidized metallic debris. Begelinger and deGeedid not result in low friction typical of boundary-lubricated 1191 have observed that a drastic decrease in friction and wearsurfaces, but the presence of water vapor and oxygen was occurred when the oxygen concentration in the lubricant wasfound to be effective. They interpreted that a strongly an- increased. They postulated that oxidation of the asperity con-chored tenacious soap film, a few molecules thick, was formed tacts prevented the formation of metal-to-metal contactsdue to a complex chemical reaction between the fatty acid wherever the lubricant layer was penetrated by the surface ir-molecules and a thin oxide surface layer. Tingle (121 has of- regularities. Similarly, in a recent study in boundary lubrica-fered similar interpretations for boundary-lubricated metal tion [201 it has been shown that an optimum value for thesurfaces with fatty acids in solutions. Lubricated experiments amount of oxygen in the lubricant exists for which minimumwith copper-beryllium alloys have shown that for a given load wear occurs. When this value was exceeded a transition to athe degree of intimate plastic contact was greater for softer regime of high wear resulted, apparently due to the rupture ofalloys 113). Accordingly, it was suggested that the increase or an appreciably thick oxide.decrease in the coefficient of friction with subsurface hardness Blouet and Courtel 1211 slid pure aluminum on tool steels
submerged in different lubricants and discovered that theConwbuittd by the Thbology Divsion to pubicaton in the Jovppi,., op coefficient of friction and the wear rate decreased significantly
Tmmotoo. Manucript reiived by the Tnbology Divi son. Augusi is. ie$. when the thickness of the aluminum oxide reached a critical
5021 Vol. 106, OCTOBER 1986 Transactions of the ASME
28
Ivalue of 70 rm. Experimental work on aluminum alloys slid oxide films can minimize plastic deformation and thus frictionagainst steels in lubricants has also shown that aluminum ox- and wear. In particular, this paper addresses the prevail-ide had a marked effect on both fric tion and wear (22, 231, in- ing friction mechanisms of oxide-covered metal surfaces independent of oxide thickness and subsurface alloy. This is in boundary lubrication, and presents experimental results basedcomplete disagreement with previous studies where the oxide on which an analytical model for friction, when the oxide filmthickness and the subsurface hardness were stated as impor- is not ruptured, is obtained. In addition, several possibletant parameters for the effectiveness of the oxide film [I, 4, 6, failure mechanisms for thin and thick oxide films are pro-71. It was also found that removal of the magnesium oxide, posed.which was considered to be a solid lubricant, with an am-monium salt solution produced higher friction coefficients. 2 Experimemua ProceduresHowever, this was not found to be the case in a different study 2.1 Materals. Pure aluminum, OFHC copper and chro-with similar aluminum alloys without lubricants, where it was *um (1S urm thick electroplated on AISI 1095 steel) werereported that the coefficient of friction was not affected by the h os for thi est iat on Aep iary sons for emagnesium oxide layer [24]. chosen for this investigation. The primary reasons for this
In the past, the friction of oxidized surfaces in lubricated choice are the availability of sufficient information on the ox-sliding was explained on the basis of the conventional model idation kinetics of these metals, and the marked differences inslidng as eplanedon te bsisof te cnvetionl mdelthe mechanical properties (e.g., elastic modulus and hardness)for boundary lubrication (251. It was argued that friction was the erhanical ro ter i es. e a lus and cop-low because of the reduced interfacial shear strength of the of the three metals and their oxides. The aluminum and cop-
Table I Properties of Experimental MaterialsMaterial
Property Aluminum Copper ChromiumHardness before annealing (MPa) 294 * 52 1,363 * 53 6,590*284Hardness after annealing (MPal 186*16 510*21Oxide hardness (MPa) 19,6136 1,7165 15,690 b
Oxide-metal hardness ratio for:a. Metal hardness before annealing 66.71 1.26 2.38b. Metal hardness after annealing% 105.44 3.36 -Density (g/cmJ ) 2.70 8.96 7.19
Molas volume (cm3) 9.99 7.09 7.23Oxide density (S/cm3) 3.97 6.30 5.21Oxide molar volume (cm3) 25.68 12.62 29.17Oxide-metal molar volume ratio 2.57 1.78 4.03'fReference 141bEstimated
oxide-covered asperity junctions. This friction model, how- per specimens were annealed for an hour at 673 K and 873 K.ever, does not account for some important parameters, such respectively, in an argon atmosphere before oxidation. Table Ias the thickness of the oxide film and the elastic moduli of the lists the experimental materials and their properties.oxide layer and the metal substrate, which have been stated asimportant in other studies. Moreover, recent work in bound- 2.2 Oxidation of the Specimens. After polishing the pin andary lubrication has addressed the limitations of the conven- the disk specimens to obtain a mirror finish, they were cleanedtional boundary lubrication model and has shown that the with soap and warm water, rinsed with methanol and acetone,predominant steady-state friction mechanism is plowing [261. dried in air, and then oxidized in a furnace. The oxidationFrom the wear point of view, it was also shown that the temperatures were so selected that oxide layers of a wide rangeprimary wear mechanism of boundary-lubricated metal sur- of thicknesses could be obtained. After an hour of oxidationfaces is an abrasive-type mechanism 1271. These studies in at a given temperature, the specimens were furnace cooled toboundary lubrication have indicated that the prevailing fric- room temperature to minimize cracking of the oxide layerstion and wear mechanisms can be minimized if plastic defor- due to thermal stresses. The temperature of oxidation %asmation at the sliding interface can be made to vanish, maintained to within 4"C. Table 2 lists the temperatures of ox-
The aim of this study, therefore, is to investigate whether idation for each metal, the corresponding calculated oxide
Nomenclature
-A - preexponential factor k = ellipticity parameterC - constant m,n = constants
E.E,,E, - elastic moduli p = pressure 6 = stoichiometry ratioE' - effective modulus p. = actual pressure at center i0 = viscosity at ambientF - tangential force of contact pressureL - normal force pa = maximum pressure in X = lubricant thickness to
M,,M, - molecular weights Hertzian contact surface roughness ratioQ - activation energy r = distance from centerline A = coefficient of friction orR - radius of pin, radius of s - lubricant shear strength traction ratio
cylindrical asperity, or I W time -,,V, = Poisson's ratiosgas constant U= velocity = oxide layer thickness
T - temperature = function of oxygen par- , = densitiesV., V. - molar volumes tial pressure Subscripts
a - half contact width = function 3f temperaturea, - half contact width of -- contact area ratio (eo/a) I = layer
Hertzian contact 0 = pressure ratio (o,/Po) me = metalh,..h, - minimum and central - = viscosity-pressure ox = oxide
lubricant film-thicknesses coefficient s - substrate
Journal of Trlbology OCTOBER 1986, Vol. 1081503
29
Table 2 Oxide film thlckness and surface roughaess for m, hour of oxidationin air
Metal Oxidation Calculated Oxide Centerline averagetemperature thickness roughness
(K) (tum) (,m)
Aluminum 373 4.2 0.05473 7.0 0.137573 7i.0 0.146673 15.6 0.152773 68.5 0.15
Copper 408 7.0 0.1433 9.0 0.1445 10.0 0.53513 12.5 0.11555 30.7 0.3673 208.0 0.28
Chromium 773 28.2 0.05973 126.6 0.1I173 926.3 1.22
thicknesses and the measured centerline average surface on the pin-on-disk tester. The tested specimens were cleanedroughnesses. The details of calculations are given in the Ap- again after the experiment with warm water and acetone andpendix (equations (A4)-(A9)). stored in a container with Ca 2SO 4 at room temperature.
Depending on the experimental scatter at least three tests were2.3 Lubrileat. In order to avoid complications from the conducted in each case. All tested specimens were observed in
formation of boundary films, which may result from chemical an optical microscope. Some of the specimens were cleanedreactions between the lubricant and the surfaces during slid- with acetone in an ultrasonic cleaner for a few minutes anding, a relatively inert additive-free mineral oil was used. The then were observed in a scanning electron microscope. A sur-oil was primarily a mixture of naphthenic hydrocarbons. face profilometer was used for obtaining the centerline a"-Table 3 lists some properties of the mineral oil. erage surface roughnesses of the oxidized and worn surfaces.
The diamond stylus of the profilometer had a tip radius of 2.5Table 3 Properties of the lubricant &m and the stylus force was 0. 1 g. The scanning speed was
viscosity at 310 K 74 cSt about 1.5 mm/s.Viscosity at 372 K I I cStDensity at 298 K 0.886 g/cn 3
Flash point 455 KSurface tension at 298 K 26.9 dyn/cm 3 Experimental Results
3.1 Aluminum. As Fig. I shows, the coefficient of fric-
2.4 Experiments. A pin-on-disk tester was used to conduct tion of the nonoxidized aluminum was initially about 0.45 andthe experiments. The experimental apparatus has been de- then it decreased rapidly to a steady value of 0.2. The initialscribed in detail in a previous publication [261. The normal coefficients of friction of the oxidized aluminum surfaces.load was 2 N. but tests were also conducted with loads in the however, were significantly lower, in the range 0. 3 to 0.25 (ex-range 0.02-1 N. The angular speed was 4.5 rad/s and the cept in the case of the aluminum oxidized at 773 K for which itlinear speed was between 0.6 and 3.5 cm/s. All tests were con- was high, about 0.4), and the steady-state values were onlyducted in laboratory air at room temperature. marginally lower, between 0.15 and 0.2. Roughness mea-
Before each experiment the oxidized specimens were rinsed surements of the oxidized surfaces have shown that the surfacegently with methanol and acetone, dried in air and then tested roughness increased with the temperature of oxidation (Table
6 /
04, 67- X
W00
U._
U. .. . .
t.- ',I. -- - T
U_ . .. V -- !-
o0' - - C_.- - :- "
SLIDING DISTANCE,
Fig. I Coefficient of fe llon "vwe sllqag dlalance for nnoxidlmdn o0idlnsd aluminum siraes lild on themselves flubftsated as.
perlmnta, normal load a 2 N)
504 1 Vol. 108, OCTOBER 1986 Transactions of the ASME
30
I £
2). The increase of the initial coefficient of friction with the contrast with the nonoxidized surfaces. Figure 3 shows theoxidation temperature may be attributed, therefore, to the ini- worn surfaces of aluminum specimens oxidized at 673 K aftertial surface roughness. The friction curves of the aluminum the transition. It is evident that the surfaces have undergoneoxidized at 373, 473, 573, and 673 K show a transition from a severe plastic deformation and that the interfacial contact waslow friction to a relatively high friction regime. By contrast, primarily intermetalic. In the case of the specimens oxidizedthe friction curve for the specimens oxidized at 773 K shows at other temperatures similar observations before and after thethat initially the friction coefficient assumed very high values transition were made. However, for the aluminum oxidized at(the maximum was about 0.96) and eventually a steady-state 773 K the topography of the worn surfaces was similar tovalue of 0.17. those of Fig. 3, even for extremely short sliding distances.
Representative micrographs of the worn disk and pin sur-faces, which were oxidized at 673 K, are shown in Fig. 2. 3.2 Co . The coefficients of friction of the nonox-Although a few narrow plowing grooves have formed on the idized and oxidized copper are shown in Fig. 4. For the nonox-surfaces plastic deformation did not occur at every location, in idized copper the initial coefficient of friction was 0. 18 and the
steady-state value was 0.17. The initial coefficient of frictionof the oxidized copper assumed values between 0. 12 and 0.2depending on the roughness of the oxide layer. Surface pro-filometry of the oxidized copper surfaces demonstrated thatthe roughness increased due to oxidation (see Table 2). For ex-ample, the highest initial coefficient of friction was about 0.2and was obtained with copper specimens oxidized at 445 K,the temperature for which the roughest oxide was formed.Marginally lower steady-state coefficients of friction, between0.09 and 0.15, were found for the oxidized copper.
Scanning electron micrographs have shown that surfaceb plowing occurred at the initiation of sliding. More and rel-
SWIMp atively large grooves were formed on the nonoxidized coppersurfaces and on the copper with thin oxide layers. Examina-IFi 2 Wow trcka of aluminum surfaces oxidized at 673 K: (a) disk and tion of the plowed surfaces with a profilometer indicated that
(h) pin (nomW load. 2 N, distance 9 = 17 m) the depth of the grooves was larger than the thickness of the
I --I '__
FIg. 3 Ww trscks of sluminum surfaceS oxidized t 673 K: (*) disk and(b) pin (normal load - 2 N, distance slid = 29.5 m)
03- O ,Zd -
-X- - -
8 o1 £ " --- ---_
SLIDING DISTANCEmFig. 4 Coefficient of friction "rsus slidlng distance for nonomledanW oxkllm pnowsuacoa sld on 1mmolvU Outif.ated sqpe.Iim ta. nomal Noad a 2 N)
Journal of Tribolog3 OCTOBER 1986, Vol. 1081505
oxide layer. However, in the case of the thick oxide layers
(e.g.. 31 and 208 am thick) many grooves with depths less thanthe oxide thickness were also found. It appears, therefore, thatplastic deformation and complete rupture of the oxide layer
occurred at the initiation of sliding only in the case of the thinoxide films.
Figure 5 shows numerous plowing grooves on both surfaces.Rupture of ridges formed due to plowing, and wear debris for-mation is also noticeable in Figs. 5(a) and 5(c). Typicalmicrographs of worn surfaces oxidized at 555 K are shown in msFig. 6. It is evident, by comparing the surfaces shown in Figs.5(s) and 6(a). that fewer plowing marks have been formed onthe disk surface of Fig. 6(c). possibly due to the protectionagainst plowing provided by the thicker oxide. However,many plowing grooves have been formed on the pin surface(Fig. 6(b)). This may be attributed to the continuous contact Iof the pin during sliding, in contrast to the disk surface wherecontact with the pin occurs at any location only once in eachrevolution. Thus, plastic deformation and removal of the pro-tective oxide layer may have occurred initially on the pin sur- Iface and much later on the disk. Figure 6(a) is an example of
FW 08 Wowr oafs@ coppar surfaces oxidized at US5 K: (a) disk and M~pin (normalld 2 N. distance slid - 23 m)El .the partially removed oxide film. The figure also shows oxideislands on the sliding interface which have survived rupture Iand locations where the oxide has been removed. Similarobservations were made on copper oxidized at 673 K.
3.3 Chromium. Figure 7 shows the friction coefficients of- the nonoxidized and oxidized chromium. The nonoxidized
chromium produced an initial coefficient of friction of 0.2 andafter 0.5 m of sliding it attained a maximum of 0.35, A steady-state value of 0. 15 was reached after 5 m of sliding. The fric-tion curves of the oxidized chromium are substantially dif-ferent at the very beginning of sliding. However, the steady-state values of the oxidized chromium were very close to the
4W steady-state friction coefficient of the nonoxidized chromium.about 0.15. The most interesting result was that the coeffi-~cients of friction increased with the oxide thickness; the coef fi-
I Wwtrcksofcopper aI oaszldldat ANK: 4)disk.,h)pim cient of friction of the thinner oxide formed at 773 K wasand e)l hgermagnIfce* of pin sface (nomal load 2 N, distane markedly lower than the friction coefficient of the nonox-
li d 3 HO idized chromium until a steady-state was reached. Then it re-
06 :ROMIUMI
.04-
06
o2 - --" ' -
-1
O ,- ...... I
.. . . .I.- . . ...-- - - '-
OiI01 10 1U
SLIDING DISTANCE. m
Flg.7 CoslelcenI of Wion versus sliding distame for nonoxldldand oxidaci atwelaum euwoo sld on Wameaoves Puhaietood ex.
56I, Vol. 108, OCTOBER 196 Transactions of the ASME m32
mained constant and was slightly lower than the steady-state before the maximum coefficient of friction was reached (i.e.,coefficient of friction of the nonoxidized chromium, i.e., before the transition from low to high friction). By contrast,about 0.13. Fig. 9 shows that plastic deformation and groove formation
Scanning electron microscopy and surface profilometry in- took place on both surfaces. The micrographs have been ob-dicated that the surface roughness increased with the oxide tained after the maximum (about 0.35) coefficient of frictionthickness (Table 2). The differences in the initial coefficient of was reached and after a steady-state value of 0.14 was at-friction can be associated, therefore, with variations of the tained. The surface topography of the oxide layers formed atsurface roughness as a function of the oxide film thickness. 973 and 1173 K was similar to that of Fig. 9 even for extremelyAll oxidized surfaces were green, but those oxidized at 773 K short sliding distances. It was also found that the surfaces ofretained the initial mirror finish. The oxide film produced the chromium pins which were oxidized at 973 and 1173 K suf-after oxidation especially at 1173 K, was quite darker and fered severe plowing and rupture of the oxide film almostduller than the other two cases. within the first revolution. Plastic deformation and plowing of
As in the case of aluminum, the thinner chromium oxide the disk surfaces, however, was noticeably mss than that of theshowed a transition from low to high friction and wear. pin surfaces.Micrographs of the low friction-wear regime obtained for dif-ferent sliding distances illustrated that initially, when the coef- 3.4 Expeats With Light Loads. To investigate theficient of friction was about 0.12, the surfaces did not show significance of the normal load on the friction and wear be-any evidence of plastic deformation. However, after relatively havior, experiments with loads in the range 0.02 to I N wereshort distances of sliding a maximum value of 0.31 was also conducted. One of the striking findings was that for a cer-reached and many plowing marks formed on the surfaces, tan material, oxide thicknes and load combination, plasticeventhough the coefficient of friction reduced eventually to a deformation of the sliding pairs was negligibly small. In addi-low steady-state value equal to 0.13. Figures 8 and 9 show tion, the magnitudes of the initial coefficients of friction withcharacteristic micrographs of chromium oxidized at 773 K ob- loads less than or equal to I N were noticeably lower thantained from the low and high friction regimes, respectively, those obtained with 2 N. However, the steady-state valuesFigure 9 shows no evidence of plowing on any of the surfaces, were only marginally lower than those obtained with the 2 N(The cracks on the su,.ices were observed on all the chromium normal load.surfaces after oxidation.) The micrographs have been taken Figure 10 shows the initial coefficients of friction for the
load range 0.02 to 2 N. The figure shows a general trend forlower friction up to I N, and higher friction at 2 N. The reduc-tion of the initial friction coefficient is more significant for ox-idized aluminum than for oxidized copper and chromium.This discrepancy may be due to the removal of the oxide filmfrom the copper and chromium surfaces, especially for therelatively heavy loads. It is also worth noting that the initialcoefficients of friction of the nonoxidized surfaces are, ingeneral, lower than those of the oxidized surfaces perhaps dueto the rougher surfaces of the oxide layers. This appears to be
* 'more significant in the case of very light loads (less than 0.52 m N). A possible reason for this discrepancy may be the instan-
taneous flattening (i.e., deformation) of the oxide undulationsdue to the heavy loads, in contrast to the case of the Jightloads.
*Figure I I shows the steady-state values of the coefficient offriction versus load for both nonoxidized and oxidized sur-faces. The results are scattered and, thus, cannot be consid-
Ud! o
Flg. I Wol ad of omkam swise oxiad at 773 K: (a) disk,() j ':pn, (0 and 14 hlgl nmsuulolatlon of disk and pin surfaces, reope.liol (mnill od .2 N, s 0tu Unomluttone of sldino ,
3q
I I'tI' I .z
t Fig. t0 Inti oceficients of vrc us load for nonoxidld andFIg. S Ww tracks of chromium surscoee oxodtid at 73 K: (a) disk and oxidtd slunnum, copper, and chromium surfaces slid on themseolves0) pin (normal ION.a 2 N, dietance Old a 2.3 m) PubIcated expdnmons)
i Journal of 'ribology OCTOBER 1986, Vol. 1081 SOT
T T
0IOs I II I
0
. oMfN t $73 9
u. 0 K.hld II 613 K00O.4,11ZW ?713Kt
h COPPER
in 05 - A w,ft of 673K
CHROMIUM
i So00.h4' IIo 973K
0-
00LOAD. N
" 00 . . . +~o . .
i. 11 Slo4dy-tato offpclemt olcOW Versus loa fr mxk n o.Idtdand oxldtnd aluminum. coper, ad chromum mild on
uemmalv (lubricsld expeiments)
b
FI 12 Wow Week$ of p ewrace1 ox- at 673 K: (a) disk and0) pin (niomal load ,, 0.0 N, detnce slid SS m)
ered conclusive due to almost complete rupture of the oxide Ilayers when the steady-state friction was attained. The some-what lower steady-state friction values obtained for light loadsmay be attributed to less plowing of the surfaces as opposed to bmnds ofI
the steady-state friction values for heavy loads (e.g.,for 2 N) -ea, tfikck
where severe plowing occurred. Indeed, surface micrographsof the worn surfaces showed fewer and significantly smaller GLUM,grooves on the surfaces for sliding with light loads. F 1 W ee racks of chrofMum surfaces oxidized at 073 K: (a) disk.
Figure 12 supports the validity of the above remarks. The (b) her mapilftcafu of das surface, and (c) pin (nomal fod a 0.2
micrographs of this figure were obtained after sliding copper N, diOSice sid a a m?oxidized at 673 K on iself for 55 m with a load of 0.05 N. Twoplowing grooves can be seen on the disk surface (Fig. 12(a)). altered at all and micrographs similar to that of Fig. 8 were ob-However, despite the relatively large distance of sliding the tained. Figure 13, for example, shows the surfaces ofrest of the surface is still covered with the oxide layer. More, chromium oxidized at 973 K and slid for 68 m under a load ofand relatively smaller grooves have formed on the pin surface 0.2 N. Neither the disk nor the pin surface shows any evidenceas shown in Fig. 12(b), due to the continuous contact of the 6f plastic deformation. Figure 13(b), which is a higherpin surface which resulted in severe plastic deformation and, magnification of Fig. 13(a), shows that only burnishing hasthus, removal of the oxide film. Nevertheless. the number and taken place wherever contact was established. The worn sur-size of the plowing grooves, as well as the width of the wear faces of the same materials but under a load of 2 N weretracks ae slgnificandy smaller than those obtained from the similar with those of Fig. 9 even for very short sliding Uexperiments with 2 N. distaces. It appears, therefore, tha under the 0.2 N load the
The most promising experimental results were found in the deformation at the contact interface was pritrily elastich -case of chromium. It was found that under light loads low dfriction coefficients, about 0. 1 or less, and practically no wear 4 Amayds nod Discsaomoccurred. This was found to be the case even for the thick ox- Aides for which high friction and wear were found for 2 N. The It has been proposed in the past that low friction and mild
oxidized surfaces appeared to have deformed only elastically wear can be obtained when the oxides are hard and easilyin contrast to the nonoxidized surfaces where plastic deforma- shearable (l, with thicknesses larger than a critical value It 3tion (plowing) occurred even for very light loads. The to- 41. But easily shearable oxides are soft and thus they cannotpography of the surfaces after large sliding distances was not resist penetration during sliding. The experimental work of
5061 Vol. 108, OCTOBER 196 Transeetlons of the ASME n
Itthis investigation has demonstrated on the contrary that oxidefilms of any thickness may be effective depending on the nor- F
mal and tangential surface tractions. It has also been argued -tthat the relative hardness of the oxide to the metal substratecontrols the deformation at the oxide-metal interface and thusthe disruption of the protective oxide layer [6, 7, 131. How- iub'.Caft
ever, when the oxide is not ruptured during sliding, the oxide-oxide contacts deform primarily elastically and the interfacial ' 1 .-. . .
stresses and strains depend on the elastic properties (e.g.,modulus of elasticity) of the oxide and the metal subsurface, ubSt r a.Is E.and the thickness of the oxide layer. U
It is evident, therefore, that the friction and wear mech-
anisms associated with oxidized metallic surfaces in lubricatedsliding must be analyzed in terms of the appropriate parame-ters when the deformation mode of the interfacial contacts iselastic or plastic.
4.1 Friedom Coeffidet Whe. The Deformadon ModeIs Ehulc. It is evident from Figs. 8 and 13 that when the oxide Fig. 14 Model of Contlt bowe a slatioan rtgid cylindftcl aetyis not removed, plastic deformation and wear of the sliding a" a Sliding elasti c layered miumsurfaces are virtually insignificant. Under these conditions,the deformation of the sliding contacts is elastic. The ex-perimental friction coefficients for this case were in the range and a,, rigidly adhered to an elastic half-space with elastic-0.1 to 0.2, which are typical of boundary-lubricated surfaces, properties E, and P,, The elastic medium is loaded by anMoreover, the lubrication regime can also be defined in terms asperity, which is assumed to be rigid and cylindrical. From
of the ratio of the lubricant film thickness to the combined the Herzian solution for homogeneous and isotropic media,surface roughness, X. For the pin-on-disk geometry the the normal pressure at the asperity contact can be expressed asminimum and central film thicknesses, A. and A, can be ob-tained as 281 [ (_ .)P1 [I
hw = 3.63RU °-UG 4 9 W- 0 073(I - e-°.0k) (I) ) = PoI/- (3)
AlI-2.69RU 0-6G 05 ' WO0r07(- 0.61 -o.3k) (2) where Po is the maximum pressure along the centerline of thewhere, contact (i.e., at r = 0), r is the distance from the centerline and
whereL a is the half width of the contact given byU- G° G=-yE' W= l,,E'R E'R 2
0 = 2 [LR(-) 14)and R is the radius of the pin, qjo is the viscosity at ambient L E I
pressure, v is the sliding velocity, -y is the viscosity-pressure where L is the normal load per unit length (normal to the Xy-coefficient, L is the normal load, E' is the effective modulus plane), R is the radius of the cylindrical asperity, and E and go,of elasticity (=E/(l - P2 )), and k is the ellipticity parameter are the elastic modulus and Poisson's ratio of the half-space.which is equal to 1.0339 for a sphere on flat type of contact In th. .se of layered media, however, the stresses and(281. strains .: .e from the Hertzian solution, depending on the
Because the micrographs and surface profdes of the nonox- ratio of •- .lastic moduli of the layer and the substrate, andidized surfaces have shown plowing and plastic deformation in the ratio -he contact width to the layer thickness [29-321.all cases, only the lubrication regime of the oxidized metal sur- For moderate values of the ratio of the elastic moduli Guptafaces needs to be identified. The most likely case for elas- and Waiowat [311, for instance, have proposed that the pres-tobydrodynamic film lubrication corresponds to the ex- sure at the contact of a cylindrical indenter and a layeredperiments conducted with the lightest load (0.02 N) and medium can be approximated fairly accurately as a weightedhighest sliding speed (3.5 cm/s). For these values of L and v, sum of elliptic and parabolic functions, i.e..and for E = 4.14 x 10"1 N/m 2 and , = 0.25 (which aretypical values for oxides), and R - 3.175 mm (radius of pin), ='o' - l-the following values of hw and h, were calculated from equa- p 8 3 t ations (1) and (2) l -- i
hken =0.0196pm h'0.0346JAm r 2
On the assumption that the roughness values of the pin sur- +4(0- -a) Ij(faces are the same as the roughness values of the disk surfaces
(Table 2), the estimated film-thickness values for A. and h, where a - ao/a, = P./Po. and a and p, are the actual halfare sigificantly smaller (in most cases by an order of mag- contact width and actual normal pressure at r = 0, respec-nitude or more) than the combined surface roughness. For ex- tively. It is reasonable to assume moreover that the aboveample, the largest value that the ratio A can assume is 0.49 and solution is also valid when small tangential tractions, typical
is obtained for the roughness value 0.05 am (i.e., combined of boundary lubricated surfaces, are present at the contactsurface roughness of 0.071 iam) and film thickness of 0.0346 interface.am. It can be concluded, therefore, that X < I and that sliding The friction force will then arise primarily from shearing ofof the elastically deformed oxidized surfaces occurred in the the lubricant film. Thus, if s is the shear strength of the lubri-boundary lubrication regime, cant film, the friction force per unit length, F, will be
The elastic boundary-lubricated sliding contact can be ideal- F = s dr - 2as (6)ized as shown in Fig. 14 and expressions for the coefficient offriction or, more appropriately, the traction ratio can be ob- The normal load per unit length, L, can be expressed astained from a Hertzian-type analysis. The figure shows anelastic layer of uniform thickness, f, and elastic properties E, L - 21op(r) dr (7)
Jurnal of Tdbology OCTOBER 1986, Vol. 1081W135
Substituting the expression for the pressure p(r) from equation 2, 4 and 8 are appropriate for oxide layers and metallic(5) in equation (7) the normal load L per unit length can be substrates.written as Moreover, the parameter which primarily controls the mag-
nitude of the coefficient of friction is the ratio s/p. Lower
21/2 s/p ratios can reduce the coefficient of friction to 0.05, or!! J I (-9 -even less. This suggests that extremely low friction coefficients
a i' could be obtained in boundary lubrication if the contact- pressure can be increased significantly, but without surface
plastic deformation. Figure 10, for example, shows that the
coefficient of friction of the oxide-covered metal surfacesassumes relatively lower values when the load, and hence the
(8) contact pressure, was increased. However, in the case of heavya Jloads (2 N) the coefficient of friction was high due to plastic
deformation of the surfaces. This is evident from the micro-
and after integration of equation (8) the normal load L is given graphs of the surfaces slid under 2 N.by The effect of the lubricant shear strength, s, on the coeffi-
cient of friction is equally important. It has been reported that
La-- a (AP. (9) at low pressures the lubricant shear strength is approximately2 "constant but at high pressures it increases with the pressure in
a roughly proportional manner (33, 34). Rabinowicz haswhere p, - Op o argued that the ratio s/p, where p is the hydrostatic pressure,Then, the coefficient of friction, M = F/L, can be obtained by obtains a value of about 0.1 when p is low and about 0.05dividing equation (6) with equation (9) as when p is high (341. In view of the proposed range for the 3
4 # 'values that the ratio sip may obtain, the friction curves for(~-~.- (10) s/pa = 0.05, 0.1, and 0.2 are also shown in Fig. 15. (Because
of the difficulties associated with integration, it was assumed mEquation (10) indicates that the coefficient of friction is a that s/p, is of the same order of magnitude as the mean value U
function of the ratio s/p, and the ratio O/cr which accounts for of s/p.) U
the deviation from the Hertzian solution. The parameters C9 A comparison between theoretical coefficients of friction,
and 0, however, depend on the ratio of the layer thickness to as given by equation (10), and experimental friction data iselastic properties. E, also shown in Fig. 15. The experimental friction coefficients
the half contact width, a, and the es perte (3 1 have been obtained from oxidized aluminum, copper, and Uand E,, a',, of the layer and substrate respectively [311. chromium surfaces at the onset of sliding with light loads
Figure 15 shows several friction curves as a function of the (beowu suN)aie we the ontt cang be lisme toade
dimensionless ratio J1a and for different values of s/p. and (below I N) i.e.. when the contact can be assumed to be UEIIE Th cuveswer obaind frm euaton 10)andthe elastic. The ratio of the oxide thickness to half contact width
pa/E,. The curves were obtained from equation (10) and the was based on the calculated thickness of the oxides (see Tableparameters a and B from reference 31 for the assumed values 2) and by assuming that the half contact width is I jm, whichof the ratios a and E/E, and for t = a, = 0.25. The figure is reasonable for the size of the asperity contacts. It is evidentshows that the coefficient of friction is almost constant when that the experimental data are fairly well-bounded between the 3
ga < 0.05 and when /a > 2. The friction coefficient theoretical friction curves of s/p. = 0.1 and 0.2. and thedecreases gradually as the ratio /a assumes values in the overall agreement between theoretical and experimental coef-range 0.05 to 2. When the layer is very thick (i.e., when (1 f ficients of friction is reasonably good. It may be concluded,
S1) or very thin (i.e., when e/a 0.1i) the coefficient of therefore, that when the oxide layers do not deform plastically Ifriction attains the assymptotic value, (4/v) (sip,), which or fracture, the contact is primarily elastic and the predom- !corresponds to the Hertzian solution (a = 0 = i). The effect inant friction mechanism is the shear of the lubricant film.of the elastic moduli of the layer and substrate is pronounced It must be also emphasized that the above analysis does notespecially when 0.1 < i/a < 1. In this regime the coefficientof friction decreases as the ratio E,/E, increases. In general, depend on the type of the oxides formed, but only on thethe lasic odui o oxies re eveal imeshiger hanthe elastic properties of the oxide and the metal below, the ratio ofthe elastic moduli of oxides are several times higher than the the oxide thickness to the asperity half contact width, the -moduli of metals. Hence, the curves obtained for E,/E, = i, lubricant shear strength and the pressure at the center of the
contact interface, provided, of course, that the deformation iselastic.
4.2 The Friction Mechanism When The Deformaton
Mode Is Plastic. The experimental results show that the ox-idized metal surfaces may deform plastically either at the onsetof sliding or after sliding for a certain distance. Figures 3, 5, 6.and 9 show plowing and severe plastic deformation of the sur-
E, I faces and partial or complete disruption of the oxide layer.- . Removal of the oxide layer can be due to different failure
mechanisms. The oxide can be removed due to debonding be-- ,tween the oxide and the metal. This may take place if the shear
stress at the oxide-metal interface is higher than the shear. . strength of the interface. In this case, local debonding between
_ _ _ _ _ _ _ _ the layer and the substrate will initiate plastic deformation and, .... ., ... consequent disruption of the oxide film. This mechanism oc-
Fly. IS Theaweal MeftU oetfickge corm varous ratio of oxide curs when the oxide is very thin, because the shear stress does U,,W I W t S ty half C ac w, nd- exWe ntW twtmo not decay sufficiently within the oxide and thus it is high at theIe11eIItm of eGudmid alumlinm, oopper, vW chmm oxide-metal interface. However, debonding can also occur
5101 Vol. 108, OCTOBER 1986 36 Transactions of the ASME 3
Iwhen the oxide is very thick and the interfacial pores (cavities) of sliding, due to the low resistance against penetration of thepromote crack growth. r orous oxides. However, the experimental results of the
The oxide layer can also be disrupted due to plastic defor- present investigation show that under certain conditions evenmation in the substrate. Because the oxides in general are a cracked oxide may not be ruptured. This was indeed foundharder than the metal below, plastic deformation of the sub- to be the case with oxidized chromium surfaces slid under lightstrate can occur even if the oxide layer deforms elastically, loads (0.2 N). The coefficient of friction in these experimentsThis failure mechanism is more pronounced when the oxide is was about 0. 1 and the wear of the surfaces was extremely lowthin, because of the high stresses produced in the metal sub- (see Fig. 13, for example), perhaps because the low surfacestie, tractions were insufficient to cause delamination or penetra.
It is also essential to emphasize some microstructural as- tion of the oxide.pects of the oxide, especially the porosity and microcracks. The failure mechanisms of thin and thick oxide layers dis-The coverage of the oxide on the metal substrate depends on cussed above are schematically shown in Fig. 16. The figure
the oxide-metal volume ratio, known as the Pilling-Bedworth shows failure due to: interfacial debonding, plastic deforma-ratio 1351, which represents the oxide volume divided by the tion of the substrate, penetration of the layer and substratevolume of the metal that has been replaced by the oxide. (This plastic deformation, and delamination of a porous andassumption is valid only if the formation of the oxide takes cracked oxide layer. These failure mechanisms may occur con-
place primarily through an inward migration of oxygen comitantly or separately, depending on the situation. In addi-through the oxide.) Hence, if the ratio is less than one, the ox- tion, one mechanism may initiate another one as slidingide will not cover the entire metal surface and, thus, a discon- advances.tinuous oxide will form. Alternatively, if the ratio is greater The micrographs of the worn surfaces have shown clearlythan one a continuous oxide forms. The condition for the for- that plowing and plastic deformation of the surfaces occurredmation of a continuous oxide can be written as when the protective oxide layer was removed. Under these
OXIDE . ,''or
where Vo,, M,, and P,, are the volume, the molecular weight, * / /and the density of the oxide respectively, and V,, M,,, and U_p, are the same rameters of the metal. The parameter 6 isa stoichiometric ratio. If it is assumed that the oxidesformed are A120 3, CuO, and Cr 20 3 (as quoted in much of theliterature), then the oxide-metal volume ratios are 1.28. 1.78,and 2.02, respectively; 6 is equal to I in the case of CuO and C'XD
l
equal to 2 for the case of A120 3 and Cr2O3 . Because the ratiosare greater than one, the criterion set by the relation (I1) issatisfied. This suggests that oxidation of aluminum, copper, ETAL
and chromium results in the formation of continuous oxidelayers.
Although the condition set by the relation (II) is necessaryfor a continuous oxide to form, it is subject to some limita-ions. For example, if the ratio assumes values larger than two (b)
or higher, the volume of the oxide is larger than the volume ofthe oxidized metal. Under these conditions high stresses may 1_4arise within the oxide. Kofstad (361 has reported that when a OX Ot
critical thickness has been attained fracture of the oxide due tothe internal stresses may occur, resulting in a cracked and
porous oxide microstructure. This was found to be the case in METAL
the present study with copper and chromium oxidized at 673and 1173 K, respectively (i.e., for the relatively thicker oxidesof the two metals). Moreover, micrographs of the oxidizedsurfaces have shown cracking of the oxide layers in the case of c
chromium, i.e., when the Piling-Bedworth ratio assumed the ,highest value, 2.02. Indeed Figs. 8, 9, and 13 show cracks onthe surfaces of oxidized chromium. ! 7
It is also wel known that solids with internal cracks and 0. IDEcavities delaminate when normal and tangential tractions are i . . ' .
applied at the interface during sliding. The primary fractureprocess of the thick oxides can be associated, therefore, withcrack propagation in the porous oxide structure. The thicker M,.A
oxides will contain more and larger pores than the thinner ox-ides and, thus, the cracks will propagate faster and fromdeeper locations, and finally will link up easily to producelarge oxide flakes. The high friction and severe surfacedamage obtained with the thick oxide layers in the present ex-perimental work can be attributed to the delamination of the Fig. 16 Mechanisms of oxlds lallur due to: (a) InrlalI de hndil(6)1 plastic defoonalon of the Subeinte. Jc) ponatimtion Of sae lowpre-cracked and porous oxides. Moreover, instantaneous d Putonpatic d*#o"tsueitm, &W (da)etain orus aned
penetration of the thick oxides may also occur before the onset wectcndk oxdo layer
Journal of Tribology 7OCTOBER 1986, Vol. 108151'
conditions, the significance of the oxide and metallic debris Wee, of Materials. Dearborin. Mich.. April 16-I18. 1979, Eds. Ludeta K. C..
Produced is important in friction Then the friction force Glaeser. W. A., anid RItee. S. KC., ASME. New York. 1979, pp. I -If.I I Bowden. F. P.. and Young. J. E.. "Friction of clean Metals and the In- I
arise primarily due to plowing and microcutting of the sur- 1uence of Adsorbed Films."' Proc. Roy. Soc. (London), Serie A, Vol 20.faces by the entrapped debris and the predominant steady- 19SI. pp. 311-325.state wean mechanism is an abrasive type mechanism (26, 271. 12 Tingle. E. D.. -Influence of Water on the Lubrication of Metals."
The xpeimetal ricioncoeficints whn te prteciveox- Natrure, Vol. 160, 1947. p. 710.The xpeimenal ricion oeficietswhe theproectie o- I1 Moore. A. J. W., and Tegart. W. J. McG.. "Rtelation Between Friction
ide layer was removed, were found to be in good agreement and Hades Proc. Roy. Soc. (London). Series A. Vol 212. 1952. pp.with the friction values obtained from the analytical models 452-458."ed in reference 126) and the surface topography statistics. 14 Hirix. W.. and Lancaster, J1. I..' "The Inuence of oxide and Lubricant
Filmsg on the Friction and Surface Damage of Metals." Proc. Roy. Soc. (Loop-doni). Series A. Vol. 223. 1954, pp. 324-338.
1S Bierk. Kt. 0.. "'Oxygen - An "Extreme-Pressure Agent".~' Trans. ASLE.
Vol. 16. No. 2, 1973. pp. 97-106.
From the experimental and analytical work the following Rluem= Of Oxide Films on the Friction and Wear of Fe-5% Cr Alloy in Con-trolhed Enviroinmem.s" Weow, Vol. 45. No. 2. 1977, pp. 161-176.
conclusions can be drawn regarding the role of oxide layers in 17 Wilson. J. E.. Stott. F. H4., and Wood. G. C.. "The Developmtent of Wear
bonaylubrication: - Protective Oxides and Their Influence on Sliding Frictio.Proc. ROY. Soc.(London). Series A. Vol. 369, 1990, pp. 557-574.
1. Under certain conditions, low friction and virtually in- is Lee. ft. Y.. and Eliezer, Z.. "On The Critical Thickness of Protective
significant wear may result in the boundary-lubricated sliding Film at Sliding Interfaces. " Wear. Vol. 95. 1984. pp. 163-175.19 Begelingu. A.. and deGee. A. W. J., "On the Mechanism of Lubricantu
of xid-coere sufacs.Film Failure in Slidng Concentrated Steel Contacts" ASME JousiAL of2. When the surfaces do not undergo plastic deformation, LUsasATnoN TsCinrou~oov, Vol. 9". No. 4. 1976, pp. 575-579.
the primary friction mechanism is the shear of the lubricant .20 Nakayama. K., and Okamoto. J., "Effect of Dissolved Oxygen on Fric-film Thepropsed nalyica modl fo thee sldingco i on and Wear of Copper Under Boundary Lubuicationi." rans. ASLE. Vol.fim h rpsdaayia oe o hs ldn od- 23. No. I., 1960. pp. 53-40.-
tions indicates that the coefficient of friction depends on the 21 Blouiet. .. and Courtel. Rt.. "Phases of Wear of the Aluminum, Steel
lubricant shear strength, the pressure at the center of contact. Couple in Lubricated Fnction.- Wear. Vol. 34. 1975. pp. 109-12S.
the ratio of the elastic moduli af the oxide layer and the metal 22 Overfelt. ft. A.. Wert, J. J.. and Hunt. W. H.. "The Influence of Ther-mal Oxide Charrateristics on the Friction Behavior Of Alumiunum Auto
substrate, and the ratio of the oxide thickness to the asperity Bod Shc Aloys.- Trns ASLE. Vol. 24. No. 2. 19111. pp. l153-16half contact width. The theoretical model yields coefficients of 23 Edwards. W. T.. Bhargava. V., Wert. J.. Welers. K.. and Hntm. W. Ifriction in fair agreement with the experimental friction data. H.. "The Influence of Surface Oxider Characterisics on the Friction Behaviior of
3. In general, the oxide-oxide contacts deform elastically Aluminum and Aluminum Alloys." Proc. /me. Conf. OR Wear of Materials. Sanwhenthenorml srfae trctin i lowandtheoxid laers Francisco. California. March 30.-April 1. 1991. Edt. Rhee. S. K.. Ruff. A. W.
idenr thic nrand prouse theare rupturead texi rersg and Ludema. K. C.. ASME. New York. 19111. pp. 23-30.are compact and sufficiently thick. Conversely, when the ox- 24 Sargent. L. B.. 'The Itnuence 'if Ailuminum Oxides on the Transfer of
idesarethic an porus heyare uptred asiy reultng, Some Aluminum Alloys to Steel in Sliding Contact." Lubp Lagi.. Vol. 38, No.
thus, in plastic deformation of the sliding surfaces. 10. IP"1. pp. 615-621.in 5 Bowden. F. P . and Tabor. 0.. The Friction and Lubrication of Solits.
4. Disruption of the surface oxide layer generally results in Clarendon Press, Otiord. 1958. pp. .119-221.Uhigher friction and severe wear. The oxide and metallic wear 26 Komnvopotilos. K.. Saks. N.. and Suh, N4. P. "The Mechanism of Frsc-debris produced is entrapped at the interface and plowing and tion in Boundan Lubrication."~ ASME JotURNAL of TaDoLwcY. Vol 107. 1985.
nsicrocutuing of the surfaces occurs. Under these conditions. Pp. 452.42.thefritio foce ries redminntl fom lowng nd he 27 Komvopossfos . K.. Suh. N4. P.. and Saks. %.. "Wear, of Bounda&"-
the ricionforc arsespreondn tlyfro ploingandthe Lubricased Metal Surfaces." Wear. Vol. 107. 1986. pp 107-13'.wear is controlled primarily by an abrasive-type wear mech- .28 Hamrock. B. J.. and Dowson. 0. Sall Bearing Lubrication rhe
anI~m.Eiassohydrodynita cs of Elliptical Contacts, A Wiley-.Interscience Publication.John Wiley, New York. 1981. pp. 207 and 212.
29 Chen. W. T., and Engel. P. A.. -Impact and Contact Stress Analysis inAckaowiedgments Multilayer Media." t. 1. SWids Sirncluresr. Vol. S. 1972. pp. 1257- 1181
This work was sponsored by the Office of Naval Research 30 Pao. Y. C.. Wut, r.-s.. and Chu. V. P.. "Bounds on (he Maxsimum Con-tact Stress of an Indented Elastic Layer." ASME Journal of 4pptid
under Contract N00014-82-IC-0520. The personal Support Of Mechanics. Vol. 38, 1971. pp. 6-614.Dr. A. W. Ruff and Dr. R. S. Miller is gratefully ac- 31 Guipta. P. K.. and Walowit. J. A.. "Contact Stresses Between an Elastic
knowledged. Cylinder and a Layered Elastic Solid."~ ASME JousjNAL or LitruticsromTacioooov. Vol. 96. 1974. pp. 250-257.
32 Cluu. Y P.. and Hartnett. M. ,,"A Numerical Solution for LayeredSolid Contact Problems With Applica'iin tio Bearings." ASME Jou5amAs or
Releafts LVEasAnrp Tilcuposo~ov. Vol. 1035, 1983. pp. 385-590.33 Brssoe. B. J.. Scruton. B.. and Willis. F, R.. "The Shear Strength oif
I Whicalmd. J. Rt.. "Surface Deformation anid Friction of Metals at Light Thin Lubricant Films.-~ Proc. Roy. Soc. (London I. Series A.. Vol. 333. 1913.
Loads,'" Proc. Roy. Sac. fLoadon). Serie A. Vol. 201. 1950. pp. 109-124. pp. 99-l14.2 Lsess. 1. K.. "lbs Formatin of Surface Films as the Transition Be- 34 Raioiz E.. "Friction-Especially Low Friction." Fundamseais oJ
two= Mid Ad Severe Metlallic Wear," Proc. Roy, Soc. (London)I. Serie A. Tnibology. Eds. Suh, N. P.. and Salt&. N.- The MIT Press. Cambridge. MA.Vol. 273. 1963, pp. 466-43. IWO0. pp. 311-364.
3 Poom.. M. U.. Plrik, J.1I.. and Lee. It. E.. "Sliding Charctseics of 35 Pilling. N. B.. and Bedworth. ft. E.. "The Oxidation of Metals at High
146s1911 il TMMPuWistes" TMUi. AS. Vol. 3. 1960. pp. 101 - 109. Temperaiture." J. losw. Wietebr. Vol. 29. 192). pp. 5.19-591.4 liableowici, E., "Lubirkcaton of Meta Surfaces by Oxide Films." Trans. 36 Kofstad. P.. HirTemiperature Oxaaion of Metals. John Wiley, Ne".
ASLI. VoLt., 1967. pp. 400-W0. York. 1966. pp. 229-233.S Cock. K. 'Surface Oxide Fiba.w i nmeallic Contact.~. Nature.
6 Whenm ft W.. I'ilhnor of Oxde pima an Metallic Fnietjiusm." ~ AP P EN D IXROY- SM. (L111111). Series A. Vol. 212. 3952. pp. 4W0452.I
71 WhN. It. W.. "The Comtac Resistance And Mechanical Properties of bkm othOxd Fls625. anMs. rcPy.Sc.Sre . Vol. 69. 1955. pp.
I Q1110. T. F. 1.. -'The Effect Of "Hl-tSpotl' Temperatures on the The oxidation rate dt /dt of metals can be expressed approx-
tlb*" *ifWr oSOW,".' T-w. ASLE, Vol. 10, 1967. pp. 159_16& imately in terms of the oxygen partial pressure. Pa,' and the I9 96' T. P J .sa111 Sul*ie&. J. L., -A Rev"e of Oxidatmonal Wear.,. temperature of oxidation, T. as follows [AlIl
PpAN'hi Cw.!.. Ww 0"a4.s...g1 Lows, Mo. April 25-28. 1977. Ed%.ObMU, W. A- Ladowls- It C-..1111 fudsR . . K.. ASME. New, York. 1977. pp. ld I111-119,- #_ 4'Po)frkT) (Al)
S allef" . S.. J ssa * 3.J L. - ftowm,- . D. M_. "New Developmueae dtat bs ~d ~ ~Mga.'Proc. lInt. Coolf. OR where j is the oxide thickness, and 4 and 4 are functions of
-- CTOER38 Transactions of the ASME
the oxygen partial pressure and the temperature of oxidation, (c) Chromium. The experimental results of Phalnikar etrespectively. From the literature (All the following expres- al. (Al21 for oxidation in air were used in the present study forsions for the above funt tions can be quoted calculating the oxide thickness. For an hour of oxidation the
4t02) - (p021 ]1 2 < n < 8 following equations are obtained
I XTV)-exp(-Q/RT) ln = - 5,641 (-4-) + 12.9 for 773< T< 1073 K (AS)
where Q is the activation energy and R is the gas constant.Substitution of equations (A2) into equation (AlI) and integra- l~=- ( \+02 fr17<T 23K(9tion gives the following relationship for the oxide film thick- inj = - 13,003 +20.2 for 1073 < T< 1273 K (A9)
iA x( Assuming a parabolic-type of oxidation law for equationss(AS) and (A9) the following relations are obtained
where A - C(m + I) Ip02) I" and Cis a constant. E2 =4.S4x l0'exp(-22,400/RT),t for773<T<1073K(a) Aluminum. In the present study, the experimental re- k = 1.0x 10l 2exp(- S1,500/RT),t for 1073< T< 1273 K
suits reported in references [35, A2-A71 were used f6r thecalculation of the oxide film thickness for an hour of oxida- where the oxide thickness, J, is in am and the time, t, is equaltion. Thus, the following relationships for the oxide thickness, to 3,600 s.in the corresponding temperature range, are obtained The magnitudes of the activation energies are in fair agree-
ment with those reported by Gulbransen and Andrew [A131;o - 1,035(L) +6.5 for T<S53 K (M) the discrepancy may be attributed in part to the effect of the
T-6A oxygen pat) pressure which as different in each study.Nevetheess th disgremen isnot large and both investiga-
.- 7,688(L . 5 for 573<T< 873 r (AS) tions suggest that a parabolic oxidation rate law is essentially= -+6 f obeyed between 773 K and 1373 K.
Using equation (AS) and assuming a paraboic law for the ox- References of Appendiidation rate the following equation, which has the same formas equation W) for m = I, is obtained, AI Kubaschewski. 0., and Hopkins, B. E., Oxdmton of Metals and Alloys,
Butterworths, London. 1%2. pp. 35-53.Ez = S.67 x 106"p(- 30.500/RT),t for 573 < T< 873 K A2 Reference tAll. p. 3t.where r = 3,600 s and f is in am. The obtained magnitude of A3 Smeltier. W. W.. Oxdatioa of Aluminum in the Temperature Range
t400-60C " J. Soc.. Vol. 103, 19"6. pp. 2D9-214.the activation energy, 30,500 ca/ol, is in fair agreement A4 Smelr. W. w.. -PviaplApplicable to the Oxadation and Corrooswith the reported results IA3-A5]. of Metals and Alloys," Corosion. Vol. II. 195S. pp. 366-374.
AJ Gulbranwn. E. A.. and Wyw"g. W. S.. "Thin Oxide Films On Alu-(b) Copper. Based on the experimental results of ref- minum." J. Phys. and Colloid Chem.. Vol. 51, 1947. pp. 1087-1103.
erences 135, AS-A101 the following two relationships for low A6 Gulbransen. E. A.. "The Kinetics of Oxide Film Formaton on Metalsand high temperature oxidation (for an hour of heating) are and Alloys." Tr#ar. Eiectroclemf. Soc.. Vol. 91. 1947. pp 573-604.
A7 Aylmore. D. W.. Grela. S. J.. and Jepson, W. B.. "The Oxidation ofobtained Aluminium in Dry Oxygen in the Temperature Range 400-650'C." J. inst.
voekr. Vol. a1. 1960. pp. 205-206.ini 1,742 +8.5 for T< 473 K (A6) AS Rhoin, T. N.. "Low Temperature Oxidation of Copper. I. Physical
Mechanism." J. Am. Chem. Soc.. Vol. 72. 1950. pp. 5102-3106.A9 Valens. G.. "Theoretical and Exerimental Invetgations on the
Simultaneous Formation of Several Layers Danat Oxidation." Proc. Int.ln -- -6,058 + 16.6 for 473 < T< 1173 K (A7) Con. on Surface Rewcttons Pittsbursh. PA. 194. p. 156.
)AI0 Vernon. W. H. J.. "The Fomation of Protecuve Oxide Films on Cop-
Again, assuming a parabolic law (i.e., equation (A3) for per and Bran by Exposre to Air at Vmrous Temperatures." J. Chrm. Soc..m- i)equaion (7) gvesVol. 1231 926. pp. 2273-2M.m- 1) equation (A7) gives All Tylecme. R. F.. "Rev ew of Published Information on the Oxilation
4 =7.9 x l0'exp( - 24,000/RT),t for 473< T< 1173 K and Scalin of Copper and Copper-Bse Alloys." J. Inlt. Meta ls. Vol. 7.,1950.pp. 259-300.
where the oxide thickness, J, is in nm and the time, t, is equal A12 Phalnikar. C. A.. Evans, E. B.. and Baldwin. W. M.. "High Tern-to 3,600 s. The obtained activation energy, 24,000 cal/mol, is perature Scaiia of Cobalt-Chromaum Alloys." J. Efectochem . Soc.. Vol. 103.
19S6. pp. 429-438.in close agreement with the reported values for copper for a A13 Gulbransen. E. A., and Andrew. K. F.. "Kinetics of the Oxidation ofsimilar temperature range [A II. Chromium." J. Ekieochem. Soc.. Vol. 104. 19 7. pp. 334-336.
IIII
Journal of Trlbology OCTOBER 1966, Vol. 108 1 13
39
IIII
The Role of Hard Layers inK. Komopoulos' Lubricated and Dry Sliding
Mem.4SME
Lubricated and dry experiments on titanium and steel surfaces with and without TiNN. Saka sputtered coatings of various thicknesses hale been conducted. The significance ofthe layer thickness. interfacial 'friction ". magnitudes of normal and tangential sur-
N. P. Suh face tractions, and the mechanical properties of the layer and of the substrate (e.g.,elastic modulus and hardness) are critically examined. The conditions under which
Department of Mechanical Enginering. the deformation mode at the solid-solid contacts is elastic or plastic are addressed inMassachusetts Institute of Technology. light of the experimental evidence and a finite element analysis. It is shown that sur-
Cambridge. MA 02139 faces with very low friction, especially for unlubricated sliding, and practically zerowear rates can be obtained in both lubricated and dry sliding by coating the surfaceswith sufficiently thick TiN layers. Removal of the protective TiN layer resulted in
plowing, severe damage, and delamination.
1 IntroductionIt is well established now that friction and surface damage temperatures and it does not affect even the highest surface
can be minimized if plastic deformation of the material at the finish. Moreover, there is no interface, as with a coating, tocontact interface is prevented. Hard and sufficiently thick suffer debonding. The thickness of the ion implanted layers,coatings, which can withstand high stresses without plastic however, is limited to 200 nm approximately and thus this pro-deformation or fracture, are more effective in reducing fric- cess is appropriate only for sliding under light loads. Ition and wear than soft layers. For instance, unlubricated ex- By contrast, high wear-resistance coatings with good
periments with nickel and copper electroplated with adherence to various substrates and without coating-thickness
chromium, cobalt, rhenium, and rhodium demonstrated that limitations can be obtained by deposition processes such asthe wear coefficients were lower by one to three orders of sputtering, ion plating and reactive evaporation. Indeed. Imagnitude than the wear coefficients of the unplated surfaces aluminum alloys and steel surfaces subjected to rolling and
(1]. Furthermore, chemically and physically vapor-deposited sliding contacts, and cutting tool inserts experienced extremelyhard coatings, such as nitrides, carbides, and oxides, on low wear when coated with a 5 /Am thick TiN layer bymetallic and ceramic substrates have significantly improved magnetron reactive sputtering 113. 141. Similarly, radio- Ithe tribological properties of various machine elements and frequency sputter deposition of 4-5 jim thick TiN on highcutting tools 12-7). High wear-resistance coatings hgve also speed steel cutting tools increased the tool life by a factor of 2been produced by such nonconventional techniques as laser to 4 151. Also, ion-plated high speed drills with 1.5 ;&m TiNprocessing; a laser beam is used to melt a mixture of metallic produced low friction at the chip-tool interface and minimal Icompounds and bind them onto the substrate (81. wear 16). Dry and lubricated experiments with aluminum,
A literature survey has indicated that a variety of techniques titanium and stainless steel surfaces coated with 4-8 jm thickcan be successfully employed to produce surfaces with low TiC and TiN by a reactive evaporation process showed thatfriction and minimal wear in sliding. In panicullr, the the coefficient of friction and the surface damage werebeneficial effects of ion implantation on the tribological noticeably lower than the uncoated surfaces (151. In fact. fric-properties of sliding surfaces have been observed in several tion coefficients of 0. 1 or less were reported for some of thestudies [9-I I]. Ion implantation of pure iron and commercial- dry tests depending on the base material and the depositedly pure titanium, for example, has significantly reduced the layer.coefficient of friction and especially the surface damage (I ll. Although most of the past investigations have providedThe high wear resistance of the implanted surfaces was at- useful information about the significance of hard layers on thetributed to the hardened layer which lowered the friction force tnbological properties of various materials, the role of suchby minimizing plowing; the low friction, in turn, reduced the critical parameters as the layer thickness, surface tractions andsubsurface delamination and wear. Also, the friction values of the mechanical properties of the layer in relation to those ofthe ion implanted titanium were markedly lower than those the substrate, have not been explained adequately. In fact, inreported for lubricated titanium [121. In comparison with most cases the coating thickness for a certain application wasother surface hardening processes, ion implantation has selected empirically through a trial and error procedure. Theseveral advantages. It is carried out at relatively low purpose of this study, therefore, is to address these important
issues in light of the experimental evidence and the analyticalaPrestra addries: Deipitmenm of Mechamcil and Industrial Engineenng. results. Moreover, recent studies have indicated that een inUmvatrry of Illinon a Urbana-Champaugn. Urbana. IL 61SOI
Cocribtrud by the Tribolory Division lot Pubagton in the JovamIA or boundary lubrication the prevailing friction and wearTawLoo. Manuscript received by the Tnboiogy Division. June 30. 1986 mechanisms are due to plowing and plastic deformation of the IJournal of Trlbology APRIL 1987. Vol. 1091223
40 I
Imaterial near the interface 116, 171. Hence, another aim of this 240 V (bias voltage) was applied to the specimens for cleaningwork is to show that surfaces with very low friction and vir- the deposited TiN from N2 which was not combined with Ti totually zero wear can be obtained under certain conditions in synthesize TiN. The bias voltage applied to the target wasboth lubricated and dry sliding. 2,750 V.
After deposition for 15 min, the flat surface was tilted again2 Experimenul Procedures by 120 degrees and the system was cooled down for 15 min.
Then the specimens were brought again below the target and2.1 Materials sad Lubrlcat. Pure titanium (99.7 per- deposition was continued for 15 min before cooling again until
cent) and AISI 1095 steel were chosen for this investigation, the necessary time for deposition was completed. TheI The primary reason for this choice was the significance of the temperature of the specimens during deposition was less thanfriction and wear properties of these metals in many sliding 473 K. This temperature rise was due to the applied voltageapplications. A mineral oil, which was rich in naphthenic (240 V) and the bombardment of the surfaces with TiN andhydrocarbons, was used in the lubricated experiments. The primarily with free electrons from the titanium target. Afterdensity of the mineral oil at 298 K was 0.886 g/cm3 and the coating, the samples were tilted again by 120 degrees, thekinematic viscosity at 310 and 372 K was 74 and II cSt, power and the bias voltage were turned off and the mixture ofrespectively. N2 and Ar gas was pumped out. Then dry N2 was admitted in-
2.2 Sample IPrepado.. The disk and pin samples were to the system, the pressure was equalized to that of the at-obtained from pure titanium, and AISI 1095 steel rods. The mosphere and the system was left to cool down for 15-20 andisks were 2.54 cm in diameter, and the pins were 0.635 cm bfe r emo the pec imswith hemispherically shaped tips of the same diameter. After The thicknesses of the TiN films after deposition times ofcutting and machining, the titanium disks were polished with 5,e7.5, and 0.75 N were estimated to be i 0.1i and 0.0 wm,240 and 600 grit SiC abrasive paper in water. Then the disks respectively. Nevertheless, the actual film thickness wasand the pins were polished with 0.3 um a-alumina, cleaned measured with a profilometer as follows. A piece of smoothwith warm water and soap, and further polished with 0.05 um glass was loaded on the flat surface together with the7y-alumina to a very smooth surface finish. The steel disk and specimens to be coated. A small piece of Si was placed on the
pin specimens were first polished with 120. 240. and 500 grit glass surface to prevent deposition of TiN on the area
abrasive cloth and oil. The samples were then cleaned and underneath. After coating, the Si piece was removed and thepolished with 600 grit SiC abrasive paper in water. Finally. the film thickness was measured by obtaining profiles perpen-
steel samples were polished with 0.3 im a-alumina and 0.05 dicular to the perimeter of the uncoated glass surface. The
,am -/-alumina to obtain a smooth surface finish. Examination measured thicknesses for deposition for 75, 7.5. and 0.75 min
of the polished titanium and steel specimens with an optical were 0.8, 0.2. and 0.02 gm. respectively. The coatings pro-
microscope did not show any embedded SiC or A120, par- duced were golden yellow in color. Microhardnesstitles on the surfaces. After polishing with alumina the measurements with a Knoop indenter (load 0.Z45 N (25 g)) ofsamples were cleaned with soap and warm water, rinsed with titanium and steel coated with 0.8 pim TiN yielded a mean
methanol, dried in air, and stored in a desiccator with CaSO, value of 20,594 MPa (2,100 kg/mm,).at room temperature. Before each experiment the samples 2.4 Experimental Details. A pin-on-disk tester was usedwere again rinsed with isopropyl alcohol ani dried in air. to conduct the experiments. The disk was mounted on a plate
The hardnesses of the polished titanium an. steel specimens which was rotated at 4.5 rad/s and the pin was held stationarywere found to be 3,030 MPa (309 kg/mm") and 3,501 MPa in a holder. The holder was attached to a rigid arm via a flexi-(357 kg/mm2 ), respectively. ble ring on which four strain gages were mounted. The tangen-
2.3 Codadll Procedures. Reactive Sputtered Deposition tial (friction) force was measured continuously by the strainwas used to coat TiN on the specimens. The polished and gages and a recorder which was balanced and calibratedcleaned titanium and steel specimens were loaded on a flat sur- before each test. Other details of the experimental apparatusface, 15.24 cm in diameter, inside a vacuum system. A high are given in reference 116).purity titanium target (99.99 percent) of the same diameter The normal load was in the range 0.02 to 2 N. and thewas centered above the flat surface and parallel to the surfaces sliding distance was between 0.02 and 100 m. The sliding speed
to be coated. The distance between the specimens and the was kept low, between 0.87 and 3.53 cm/s, to avoidtarget was 4.5 cm and the specimens were placed within a cir- hydrodynamic effects due to high speeds. All experimentstce 7.6 cm in diameter. were conducted at room temperature (294 to 298 K) with iden-
The chamber was initially evacuated to a pressure of tical metal pairs and relative humidity 26 to 58 percent.6.6x 10-7 Tort and a high purity argon gas (99.995 percent) The wear tracks of the tested samples were observed in awas admitted at a flow rate of 36.5 cm3/Min. The pressure in Scanning Electron Microscope (SEM). Characteristicthe chamber was l0x 10-3 Toff for the deposition of the micrographs for each material combination were obtained. An
thicker TiN coatings and 16 x 10- 3 Torr for the others. To ob- Energy Dispersive X-ray Analyzer (EDAX) was also used totain good adhesion between the substrate and TiN films the check whether the AISI 1095 steel substrate was exposed dur-substrates were lightly sputter etched with argon to remove ing the tests with 0.8 Mm thick TiN coatings.any surface contaminants and particularly any native oxides.The specimens were sputtered for 30 s at 50 W, and the 3 Epetmentil Resultstitanium target for 20 min at 500 W. The titanium target wasthen sputtered for I min with argon at 500 W to produce a thin 3.1 FrIctlos. The friction coefficients of lubricatedtitanium layer, 10-20 am, on the specimens. The flat surface titanium surfaces, with and without TiN coatings, slid onwas tilted by 120 degrees and a mixture of nitrogen and argon themselves are shown in Fig. 1. Figure I(a) shows the friction(26% N2 and 74% Ar) at 10 x 10- I Tort was admitted into the curves of titanium substrates coated with 0.8 Am thick TiNsystem at a flow rate of 8.6 cm) /min. The power was then in- layers. The coefficient of friction assumed a value of 0.09 withcreased to 900 W and the system was left to attain a steady the initiation of sliding and then it remained constant. Thestate for about 10 main. Then, the flat surface was brought friction coefficient was the same even for sliding distances ofback to the initial position (i.e., parallel to the target), the 150 to 200 m. Almost identical friction values were obtainedpower was raised to950 W (5.2 W/cm2) and deposition of TiN for normal loads of 0.2 and 2 N.on the surfaces was initiated. During deposition a voltage of Figure l(b) shows the friction data of lubricated titanium
3 2241 Vol. 109. APRIL 1987 Transactions of the ASME
41
07 07z TITANIUM- TN(O8, m} z TITANIUM- TN(0O2 m)-06 006- -
U _IX 05 - r0 5 - I!IL0 .0,005Nzo 003 -.o22N004" 002
0.2- 20ON 0 2U.02
SLIDING DISTANCE m SLIDING DISTANCE, mn
Fi g . I(@) Fg 1lie)
07 . IOi,07I
z T ITAN IUM - TiN (0. 2 m) Z ! TITANIUM I00.6 006l
S-
n-. 05 4 0: 05,- .IZO TTNM- ToNO.2m)o TIANU 'IO N 1 L
Z0305N 2%
02- 022
00 . .oi
01 E 00 Ot 0 ODSLIDING DISTANCE, m SLIDING :.STANCE. mml
Fig. 1(b) FIg. 1(d
Fig. 1 Ffiction oefficienit versus sliding distance for titanium coatedwlth: (a) 0.8 pm. (6) 0.2 pm, and (c) 0.02 pm TIN layers; and (d) for un-coaltd titanium. (Lubricated expriments wilth Identical surfaces.)
with 0.2 Am TiN coatings. The figure shows several friction 0 7rcurves for different loads. A comparison between Figs. I (a) z I T;TANIUMand 1(b) indicates that for loads less than or equal to I N, the o 61- - -UNCOATED -
- COATED W TH 08,m TNfriction values corresponding to the 0.2 Am TiN coatings are U i -only slightly higher than those of the 0.8 Am TiN coatings. M o 5- "However, for relatively heavier loads (e.g., 1.5 N) the coeffi-
cient of friction of 0.2 Am TiN increased from an initial value o 4,-of 0. 11 to a steady-state value of 0.46. This marked increase in 0 I oN -
friction did not occur, however, when the TiN layer was 0.8 z 0 3- 02NN- "pm thick even for 2 N (Fig. 1(a)). -
Friction coefficient data for titanium with 0.02 pm thick - o 2L -
TiN layers are presented in Fig. I(c). An increase of the coeffi- t" 0"- - -V 7cient of friction from an initial value of about 0.2 to a value in Wo r -
the range 0.55 to 0.65 is evident, even for lighter loads (0.02 uand 0.05 N). Much higher friction coefficients resulted when 0otitanium surfaces were slid on themselves. In this case, 01 1 10 ,ohowever, in contrast to the 0.02 pm TiN coated surfaces, the SLIDING DISTANCE, mtransition from low to high friction was very abrupt. Figure Fig. 2 Foleto coffliclen Versus sliding dietance for uncoated andl(d) shows that large friction values. 0.45 to 0.55, have 0.8 Am TIN.Cted tItanium. (Unlubrfltad experets with ontcresulted from sliding lubricated titanium on itself for short sa )
disances, less than I m. These steady-state high friction values produced for both coated and uncoated titanium surfaces. Butfor lubricated titanium are similar to those reported in the as sliding continued, the coefficient of friction of the uncoatedliterature 112). titanium increased rapidly to values larger than 0.45 when a
In order to investigate friction and wear of TiN-coated steady-state value was assumed. The transition from low totitanium surfaces in dry sliding, unlubricated experiments with high friction was abrupt when the load was 2 N and gradual0.8 pm thick TiN coatings deposited on titanium were con- when it was 0.2 N. It is interesting to note, moreover, thatiducted. The friction coefficient curves for 0.2 and 2 N normal lower friction for significant sliding distances was producedloads are plotted in Fig. 2. Friction curves from unlubricated with 0.8 Am thick TiN layers. The friction data for a load oftitanium for the same loads are also shown for comparison. 2 N in Fig. 2 show that friction coefficients about 0.16 wereLow friction coefficients, between 0.1 and 0.2. were initially obtained for sliding distances less than 15 m. Thereafter the
Journal of Trlbology APRIL 198? Vol. 1091 22S
42
: 5s1 c 95 - N 8 .. n 0 7-
I080.m T,N
.. - - 0511-
z , 04L --
Z03o 0.....
02AIS, - -: -
20N
0 02 3 "0 2N
00201,,2- - 0.
o0L o,
Z AIS1 1095 - ,.N(002. 0O
Z0 1 1 0 100" .. .. SLIDING DISTANCE,m
I-- Fig. 4 Friction coefficient "vesus sliding distance for uncoated and0.8 om TIN.coaled AISI 1095 steel. (Unlubricaled experiments with Idea.
_ _ _ _ _tical surfeces.)
AISI 095i o-to the lower steady-state friction of the lubricated AISI 10953 . -= steel surfaces as opposed to the higher steady-state friction of
-- _-_--_-_ .lubricated titanium (Fig. I(d)). Indeed, Fig. 3(d) shows thatthe coefficient of friction of lubricated AISI 1095 steel assum-ed initially a value between 0.12 and 0.2, and a steady-statevalue of 0.12, for loads equal to 0.05, 0.2, and 2 N. TheseI 5 .G s--Nc .. values of the coefficient of friction are significantly lower than
Fig. 3 Friction mctflc'nt versus sliding distance #of AISI 1095 steel the steady-state friction coefficient of lubricated titanium.coated with: (a) 0.1 pm. tao 0.2 pm, and (c) 0.02 aim TIN layers; and (d) for As with titanium, unlubricated experiments on steel with 0.8uncoated AII 108I steel. (Lubricated experiments with Identicaleeafcooe.) ;m TiN have been conducted and the friction coefficients are
shown in Fig. 4, together with the curves of uncoz ted steel sur-faces. It is evident that a transition from a relatvely low to a
friction coefficient increased gradually and assumed eventual- high friction regime resulted in this case. The initial frictionly a steady-state value equal to 0.57. Furthermore, the bottom coefficient of the coated steel surfaces was about 0.15.curve of Fig. 2 demonstrates that a constant friction coeffi- However, as sliding continued, it assumed higher values even-cient of 0.15 may result even for large sliding distances when tually. In particular, when the load was 2 N, the coefficient ofthe load is 0.2 N. friction increased after sliding for about 4 m to a steady-state
Figures I and 2 demonstrate that the friction force between value of 0.6. For the 0.2 N load, the transition from low totitanium surfaces can be maintained low, when the surfaces high friction was initiated after 7 m of sliding, but the increaseare coated with sufficiently thick TiN layers. The experimental was gradual and the friction values produced were quite lowerdata show that the unlubricated friction values are higher by a than those obtained with a load of 2 N after the transition, forfactor of two than the corresponding lubricated values, but the range of sliding distances examined. The friction curves ofthey are very low for unlubricated sliding between similar sur- the uncoated steel surfaces (Fig. 4) indicate that initially lowfaces. In addition, the results have shown that lubrication af- friction, about 0.16, resulted when the load was 0.2 N, butfects the transition from low to high friction significantly after 2 m of sliding it increased to a steady-state value of 0.5.(e.g., friction curves for 2 N in Figs. l(a) and 2 for coated When the load was 2 N, however, high friction resulted withtitanium). Hence, when the sliding interface is lubricated the the onset of sliding (higher than 0.3) and the steady-state valueloads for which low friction is obtained are higher than the was 0.5. The experimental results of Figs. 2 and 4 clearly in-corresponding loads for unlubricated interfaces. dicate that when titanium and steel surfaces are coated with
Friction data of lubricated AISI 1095 steel, with and 0.8 pm thick TiN layers remarkably low (especially forwithout TiN coatings, are shown in Fig. 3. Friction curves of unlubricated sliding between similar surfaces) friction coeffi-steel substrates with 0 .8 um TiN layers are plotted in Fij. 3(a). cients, about 0.15, may be obtained.The values that the coefficient of friction assumes are in therange 0. 1 to 0. 12, i.e., slightly higher than those of Fig. I(a). 3.2 Wear. The tested specimens were observed in a scan-But, the friction curves for 0.2 and 2 N are very close. ning electron microscope and several characteristic
The coefficient of friction of steel surfaces coated with 0.2 micrographs of the surfaces were obtained. It was found thatand 0.02 pum thick TiN are shown in Figs. 3(b) and 3(c). unlike the uncoated surfaces the TiN-coated surfaces forrespectively. A comparison of Figs. 3(a), 3(b). and 3(c) in- which low friction was maintained did not deform plastically.dicates that the friction force increases when the thickness of The surfaces coated with 0.8 pm TiN did not show anythe TIN layer is decreased. For example, the coefficients of evidence of plastic deformation even for normal loads of 2 Nfriction of the 0.2 and 0.02 pm TiN coatings were in the range when lubricated. Examination of these surfaces at high0.09 to 0.19 and 0.13 to 0.29, respectively, i.e., higher than the magnifications did not reveal any change in the initialvalues obtained with the 0.8 pm TiN coatings. Nevertheless, a surface topography even after sliding for ISO to 200 m. Thetransition from low to markedly high friction, such as that tested surfaces were found to be smooth and shiny just as theshown in Figs. 1(b) and I(c) for instance, was not observed for coated surfaces. However, plowing and severe plastic defor-the TiN coated steel. In fact, a gradual increase of friction mation of the sliding interfaces, like the uncoated surfaces, oc-with the distance slid has taken place (e.g., Fig. 3(b)). The curred when the coefficient of friction was high.primary reason for this discrepancy between titanium and steel Characteristic micrographs of the steel surfi -es coated withsubstrates coated with identical TiN layers may be attributed 0.8 pm TiN from lubricated experiments are shown in Fig. 5.
2261 Vol. 109, APRIL 1987 43 Transections of the ASME
I
* U20um 401am ~
Ig. We trcks of Ilubrcated AI 10ff stel coated with 0.a Orm TIN: Fig. 7 WOW tracks of lubricated titanium coated with 0.2 om TIN: (a)(ale 0 andbl 6 in (lead-0.2 Nk (c) disk and (d) pin (Iload- 2 N).a 0.02 N, distanc slid a 45.4 mr (el disk. (d) pn and
(e) higher magnllcation of a location on the pin surface (load - 0.5 N.distance slid a U m); (0) disk. (g) pin and (h) higher m nolicalon of a 3location on the pin surface (load 1.2 N, distance slid - 1.7 in).
WM u T,
Fg. 4 Patch, ich In Iron, on AlI 1065 sleet coated with 0.8 pm TIN.(The suriae was coated with a thin gold fayer, about 0.01 pm, beforeobservation for bette resolutlon.)
Energy Dispersive X-ray Analysis of the surfaces did not show -oL-
that the disk and pin surfaces deformed primarily elastically.
Similar observations were made for titanium substrates. .
Micrographs of the 0.8 #sm TiN-coated titanium and steel sur-faces obtained before sliding showed identical surfacetopographies with those in Fig. 5. Examination of the TiN-
coated titanium and steel surfaces showed that the 0.8 gm TiNlayers were discontinuous. Small patches, rich in iron, whereTiN was not successfully deposited were identified on thecoated steel surfaces (Fig. 6). These patches may have resulted
from material deformation due to the thermal stresses pro-duced during deposition. The bright marks on the surfaces mshown in Fig. 5 are patches similar to those of Fig. 6. Never- P1. I werackl of lubi cted titanium coated with 0.02 .m TIN (&)thekss, the friction coefficients were low and the wear rates d a.n0 (c) wea sheets on the disk surface, and (d) pin (load
were virtually zero.Insignificant wear rates were also obtained after sliding
titanium and steel substrates with 0.02 um TiN coatings on Figure 7 (bottom row), for example, shows that plowing andthemselves with loads less than I N. Figure 7 shows some extensive plastic deformation of the surfaces resulted when thecharacteristic surface topographies obtained from lubricated load was 1.2 N. although the distance slid was stgnificantlyexperiments with titanium coated with 0.2 1m TiN. When the less than the former cases (Figs. 7(a) through 7(e)). Relatielyload was 0.02 N the wear of the surfaces was practically in- large wear sheets were found on the wear tracks of the disksignificant (Figs. 7(a) and 7(b)). For heavier loads, 0.5 N. the and pin surfaces. Figure 7(h), for example. shows some typicaldisk surface was slightly polished (burnished, as shown in wear sheets on the pin surface. It is evident that in this :ase theFig. 7(c), and the pin surface was slightly deformed (Figs. 7(d) protective TiN layer was ruptured resulting in high wear ratesand 7(e)). However, when the load was larger than I N. plow- similar to the uncoated titanium surfaces. Furthermore, theing and severe surface damage of both surfaces occurred. friction coefficient was about 0.46 which is t, pical for
Joumal of Trlbology APRIL 1987. Vol. 1091227
I I I iII ii
lubricated titanium surfaces slid on themselves (see Fit. 1(d)). observed, especially for large sliding distances. Again, theSimilar observations were made for steel coated with 0.2 jm wear rate in both cases was negligible. Similar observationsTiN when the load was increased. were made for loads of 2 N for short sliding distances (i.e.,Surface damage and plowing occurred when the thickness when the coefficient of friction was below 0.2). For sliding
of the TiN coating was 0.02am, even for light loads (0.02 N). distances larger than 10 m, however, severe plowing andIn fact, it was found that plowing grooves were formed on the damage of the surfaces occurred, as with the uncoated sur-surfaces at the onset of sliding, probably due to rapid rupture faces for which plastic deformation was observed with the
and removal of the thin TiN layer. The micrographs were initiation of sliding even for 0.02 N. Figure 10 shows the wearIsiailar to those obtained from lubricated titanium and steel tracks of titanium surfaces coated with 0.8 pn TiN after thesurfaces slid on themselves. Delamination wear sheets were transition of the coefficient of friction from low to highobserved on titanium coated with 0.02 pm TiN even for loads values. It is clear that the surfaces have deformed plasticallyof 0.02 N. Figure 8 shows the disk and pin surfaces of titanium and large delamination wear sheets have formed on the sur.with 0.02 pas TIN coating after sliding for 37.8 m with a load faces (Figs. 10(b) and 10(d)). The micrographs obtained fromof 0.05 N. Both surfaces have been severely damaged and TiN-coated steel surfaces when the friction coefficient wasmaterial lift off (wear sheets) can be observed especially on the high showed extensive plowing of both surfaces. A corn.disk surface (Fits. 8(b) and 8(c)). Figure 9 shows the wear parison of the wear tracks of the TiN-coated and uncoatedtracks of steel disk and pin surfaces coated with 0.02 pm TiN surfaces showed similar surface topographies when the coeffi.after 43 m of sliding with 0.05 N. Plowing grooves have form- cient of friction was high. It may be concluded, therefore, thated on both surfaces. The micrographs have indicated that rupture of the protective TiN layer, especially when the loadwhen the substrate material was titanium, plowing and plastic was 2 N, after sliding for a certain distance resulted in highdeformation were more severe than when the substrate wear rates similar to those of the uncoated surfaces.material was steel. This may be attributed to the significantlyhigher friction coefficient of lubricated titanium which 4 Analysis and Discussionresulted in high tangential surface tractions and thus high wear The experimental results of this study demonstrate that lowrates.
Micrographs of titanium and steel surfaces, with and friction (especially in dry sliding) and practically zero wear canwithout 0.8 pm TiN coatings, from unlubricated experiments be obtained when metallic surfaces are coated with sufficientlywere also obtained. When the load was 0.2 N the surface thick TiN layers. The micrographs of the tested surfaces have
topography of the TiN-coated titanium surfaces remained shown that the deformation at the sliding centacts is primarilysmooth and shiny as it was before sliding. When the substrate elastic when the TiN layers were not ruptured. In addition, thewas of steel, however, burnishing and very fine grooves were layer thickness, surface tractions (both normal and tangential)
and interfacial "friction" conditions (i.e., lubricated or dryinterfaces), were found to affect the efficacy of the TiN-coated surfaces in reducing friction and minimizing surfacedamage. The experimental evidence has indicated that thesame surface topography and low friction coefficients can beobtained even for large sliding distances, provided that plasticdeformation or fracture of the coated surfaces is prevented.The state of stresses generated at the solid-solid contacts thenis of especial interest.
Analytical solutions for infinite half-space media subjectedto normal and tangential surface tractions are well known 118,191. The stress field within an isotropic and homogeneous in-
* finite half-space due to a sliding line contact was obtained longFI 9 Wow bnek of huswcatsM AM lM sow eoae woi 0.02 Im ago by Smith and Liu [20), and for a circular sliding contactTIN: ) (i ndS) pin (loda0.06 N, distwo eIM 4 ). with hemispherically distributed normal and tangential trac-I
20--'3
FiW I* Wow sw Inoif d~i~~w4idum GO&Wl with 0.1s poram Tis)
disktoN {o sdotmm~ -o m7J A() k0MOM~w on dto olk n dm*2N
(0) pM foo a.. N, 14.em " Na29
ZtO IVol. 109, APRIL 1987 Transalctions of the ASME
45
m. w mm mm | * i I
Itions by Hamilton and Goodman [21, 221. The problem of an finite element analyses. Moreover, the present analysis ac-elliptical contact with elliptically distributed tractions was counts for interfacial friction; a "friction coefficient" value isanalyzed by Sackfield and Hills (23. 241, and recently Bryant assigned to the in erface elements which, in turn, is used for Iand Keer 1251 have extended the work of Hamilton and Good- the calculation of the shear tractions at the interface byman for the general case of an elliptical contact with sticking multiplying the contact normal stress at each node with thewithin the contact region. The literature of contact mechanics preassigned friction value.between non-conforming surfaces is recently reviewed by The layered half-space is modeled by assuming differentJohnson 1261. The main conclusion of these studies is that the elastic properties to the elements of the top rows of the finitemaximum value of the von Mises stress moves toward the sur- element mesh. The rigid cylinder was modeled with a circle,face as the friction coefficient is increased, initially tangent to the half space at 0, with 28.1 Asm radius.
In the case of thin elastic layers on half-space substrates, the The total number of nodes was 1148 and the smallest dimen-derivation of analytical expressions leads to serious dif- sions of the mesh in the x- and y-directions are of I and 0.5 Ifrculties. The problem of a thin layer on a rigid substrate has gm, respectively. A 3 x 3 integration scheme was used for thebeen analyzed by Hannah (271, but only the numerical results 8-node elements.for the contact pressure were obtained. General solutions to Sliding was simulated by imposing 0.5 prm incremental up-the contact problem of semi-infinite and layered media were ward displacements to the nodes of boundary BC followed by Iderived by Sneddon [281 in terms of Fourier Integral Trans- 0.5 gm incremental horizontal displacements to the nodes offorms. However, solution of these integrals requires elaborate boundary AB. In order to compare the stresses developed bynumerical computations. Nevertheless, numerical results for a the same surface tractions within the half-space and layeredthin layer rigidly adhered to an elastic substrate subjected to media, the mesh of the layered surface was moved upwards isurface tractions have shown a rapid decay of the stresses until the maximum contact pressure assumed a value similar to
within the layer, when the ratio of the elastic moduli of the that obtained for the half-space, but for 0.5 gm verticallayer and the substrate is larger than one and the layer is suffi- displacements. For the vertical displacement of the mesh, onlyciently thick (29, 301. Furthermore, approximate numerical the center node of boundary BC was constrained against Isolutions obtained by Gupta and Walowit [311 to the contact lateral displacement. The rest of the nodes on BC were allow-problem of a layered elastic solid indented by an elastic ed to move along the x-direction to account for the Poisson'scylinder have demonstrated that under certain conditions the effect. The analysis is based on the general purpose finite ele-solution is non-Hertzian. The complex analytical expressions ment code ABAQUS. Numerical results are presented for the Ifor the stress field within layered solids, and the tedious area below the contact (detail aOO'a' in Fig. II). For simplici-numerical computations for solution, call for different type of ty, a Poisson's ratio of 0.3 was assumed in all cases.analyses. Numerical techniques, such as finite element 4.2 Analytical Results. The Mises equivalent stress con-methods, are therefore more appropriate. tours of a penetrated elastic half-space with interfacial "fric-
4.1 The Finlte Element Model. Under the usual plane- tion" coefficients j,=0, 0.1 and 0.5 and ratio of penetrationstrain assumption, sliding at the solid-solid contact can be depth to radius of rigid cylinder dlR=0.0178 are shown insimulated by a rigid circular cylinder pressed against and Figs. 12(a)-12(c). Moreover, Fig. 12(d) shows the Mises stresstraversed on an infinite half-space. Figure I I shows the finite contours of a penetrated elastic layered surface with u = 0.1. element mesh of the elastic half-space. The mesh is refined at d/R = 0.0089. elastic modulus ratio of layer to substratethe center where contact with the rigid cylinder at point 0 is EI/E, =4. and ratio of layer thickness to cylinder radiusestablished initially. The finite element mesh consists of 326 h/R = 0.142. The elastic modulus ratio value of 4 is* ap-quadrilateral 8-node isoparametric elements and 30 interface propriate for hard layers such as TiN and metallic substrates. Ielements which are used to detect contact between a nodal The interface between the layer and the substrate ispoint on -ry' and the rigid surface. Thus, the solution does not represented by the horizontal line in Fig. 12(d). Because ofdepend on the assumed distribution of the surface tractions or symmetry, the stress contours within half of the regionthe displacements at the contact, unlike most of the previous ad8"a' are shown in Fig. 12. In order to compare the stresses I
below the contact due to penetration by a rigid cylinder loadedwith the same load, the above values of dIR were assumed so
A that the resultant normal force was approximately the same ini i ' ,,w, ] ; 'i all came.
Figure 12(a) shows that for a frictionless interface yielding
I ! - - ,.,
I I 4 - -, I
C 7
WS', E uv S"QESI I II o
F,[N TE ELEMiENT IIE FIg. 12 Mh1ee allenct nlo 's due to penetration of a half-spa e eawlooWell O.0170, fo (ei =1O (6) p =0.1 and (c) p =1O.S) and
I. I Fin,,esenmnt mesh tor t , elastic hal,.ace and layered Id Ps Itt oftf eta layered stece (dIfR a0.00111. ,0.t. 01,E, -lendSurace Wil R 0.1424. (Stresses we In OPf.)
Journal of Trlbology46 APRIL 1987, Vol. 1091229
Ilayers deposited on titanium and steel, the yield strength of the
,/' -"\ C' 2 layer is about an order of magnitude higher than the yieldAN ES ,wv S."\\ strergth of the substrate. Thus, the deformation mode will be
2"~ 03 elastic provided that the thickness of the layer is sufficient (or30 the stresses to decrease to such magnitudes that yielding in the
/ substrate will vanish./ suUnder sliding conditions the stresses below the contact in-
s9 Z / crease due to the generated tangential surface tractions,especially when the interfacial friction is high. Figure 13 showsthe Mises equivat stress contours produced from penetra-tion and then slidii., of the rigid surface over a half-space withI Oand without a hard layer. The analysis has shown that in allcases the stresses assumed a steady-state after a 0.5 Amhorizontal displacement of the nodes on AB. Figure 13(a)shows that when 0. 1 the Mises stress contours are almost
IsEs EQUI STRESS 17 identical with those obtained after penetration (Fig. 12(b)).20 / This implies that the elastic stress field does not changeI 0 noticeably when the coefficient of friction is 0. 1 or less. in ac-, 2 o /cord with previous analytical studies. Nevertheless, as Fig.T ,30/ 13(b) shows, when g = 0.5 the stresses are by a factor of 2 ap-
0 • proximately higher than the stresses obtained for u =0. 1.
Moreover, the locus of the Mises stress with the highest valueI___ - _. has reached the surface. Consequently, when j = 0.5 yielding
b should initiate at the surface near the center of contact.Figures 13(c) and 13(d) show the Mises stress contours in alayered surface for the case that IA = 0. 1 and ErIE = 4. The
ratio dIR was set equal to 0.0142 and 0.0089 in Figs. 13(c) and15s Ei, STAESS 00 13(d), respectively, in order for the resultant normal force to
2 06 be the same with that of the solutions in Figs. 13(a) and 13(b).4 t- Again, the horizontal lines intersecting the stress contours5 2 4 represent the layer-substrate interface. The solutions of Figs.6 30S36 ,.13(c) and 13(d) represent cases of relatively thinS48 (hR = 0.0356) and thick (h/R = 0. 142) hard layers deposited
on the same substrate and loaded with similar loads.It is evident from Fig. 13(c) that high stresses have
developed in the layer near the contact surface. However. acomparison with Fig. 13(a) clearly shows that the Mises stress
" at and below the interface of the layer and the substrateassumed similar values in both cases, apparently because of
,LEV SRS the insufficient layer-thickness. Accordingly, the disruption ofI oc '00 c!=r the 0.02 and 0.2 Am thick TiN layers can be attributed to2 o 03 >-. -- ' " ' of t e m t ln a h
2 0£ - plastic deformation of the metal substrate near the interface.4 09 where the criterion of yielding will be satisfied. By contrast.5 S when the layer is sufficiently thick, Fig. 13(d). the stresses can
2 , ' be markedly reduced within the hard layer and thus, yielding9 24 /
'2 4 in the substrate can be prevented. Under these conditions., o30 _ both the layer and the substrate will deform elastically. In view
of the results of Fig. 13(d), the experimental evidence ac-
Pig. 13 MISS@ equ n I~i sras seurs after pecetra hn d eslidg cording to which the topography of the 0.8 Mm TiN-coated
ofa Miic suface (s -. 017 M, Mr (*I s w k I &W isldn& surfaces was the same as before the initiation of sliding can be1e011" aind eldi of a layered SiMeS (m0-0.1. EN j 4, far. (e) explained. That is, the 0.8Mum thickness of the TiN layers wasEWl-0.0 1 Nlt/[email protected], sufficient, for the applied surface tractions, to reduce theIn OP.) stresses in the substrate and, consequently, to eliminate
yielding at and below the layer'substrate interface.will initiate below the surface where the Mises equivalent stress Figures 12 and 13 demonstrate the significance of the layerassumes a maximum. Yielding will still initiate below the sur- thickness, the magnitude of the surface tractions (normal andface when the interfacial friction is low (Fig. 12(b)). However, tangential) and the interfacial friction on the stresses below thein this case Mises stresses with higher magnitudes than the fric- contact interface. Moreover, the experimental work hastionless case have arisen near at the interface. The maximum shown that the TiN layers minimized the plowing componentvalue of the Mises stress occur closer to the surface as the fric- of friction resulting, thus, in coefficients of friction in thedon at the interface is further increased (Fig. 12(c)). Under range 0.1 toO. IS for both lubricated and dry sliding. The hardthese frictional conditions yielding may initiate at the contact layer in this particular case, therefore, not only reduces theinterface. Figure 12(d), however, indicates that yielding can be stresses in the substrate but it also lowers the magnitude of themade to vanish when a hard layer is rigidly adhered to the frictional tractions. A comparison of the stress fields in Figs.substrate. In this case, the Mises equivalent stress assumes the 12(c), 12(d), 13(b) and 13(d) clearly shows how significant thishighest value in the layer which has a yield strength could be for the magnitude of the stresses experienced by thesignificantly higher than the substrate and thus, it can deform substrate. Thus, the interfacial friction (i.e., the magnitude ofelastically. Furthermore, a comparison of 'igs. 12(b) and the interfacial shear stress which may be related to the om-12(d) clearly shows that the surface hard layer has resulted in position of the materials and the lubricant) plays a significantlower stresses in the substrate. In the particular case of TiN role on the magnitude of the stresses produced below the
2301 Vol. 109, APRIL 1967 Transactions of the ASME
47
sliding contacts and, thus, it has a marked effect on the Res. Con!.. Unsiversity of Massachusetts. Amherst. MA. May 23-23. 1971.tribological properties of the surfaces. SME. pp .29-302.
6 Henderer, W. E., "Performance of Titanium Nitride coated High-SpeedIt should be made clear, however, that the primary purpose Steel Drills." Proc. Eleventh N. Am. Afanuf. Res. Coni. Linaversity of
of the presented finite element analysis is to investigate the Wisconsin-Madison. Madison. WI. May 24-26. 19"3. SME. pp. 337341.initiation of yielding below the contact interface in relation to ? Young. C. T., Becker. P. C.. and Rhee. S. K.. "Performance Evaluationsome critical parameters such as the layer thickness, the coeffi- of TN and TiC/TiN Coated Drills." Proc. Int. Conf. on Whear of Matertis.
cien offricionbetwen he hlf-pacesurace nd he rgid Reston. VA. April 11-14, 1983. ed. Ludema. K. C.. ASME. New~ York. 1983.
surface, the magnitude of the surface tractions and the i Belmondo. A.. and Castagna. M.. "Wear -Resistant Coatings by Lasermechanical properties of the layer and the substrate. An Processing," Thin Solid Films. Vol. 64. 1979. pp. 249-256.elastic-plastic analysis of a semi-infinite surface with and 9 DeanLeri G.. "Applications of Ion Implantation in Metals." Thin Solid
witouta hrd aye wil b prsened n aforhcoingpapr. Films, Vol. 107. 11913. pp 315-326.withut had lyerwillbe resnte ina fothcmin paer. 10 Smids, F. A.. et al.. 'The Use of Ion Implantation for Materials Process-
In summary, the experimental and analytical work of this ing." NRL Memorandum Report No. 5716. Nasal Research Laborator..study has shown that coating the surfaces with sufficiently Washington. D.C.. March 6. 15016.thick hard layers may result in elastic deformation at the solid- I I Shepard. S. R.. and Suh. N. P.. "The Effects of Ion Implantation on Fric
sold cntats.Undr tesecoditons lo frctin ad vr- tion and Wear of Metals." ASME iOuaNAL OF LUIUaaCArio TECHOiLocs. % 01soli cotacs. nde thse ondiion. lw ficton nd ir- 104. 1982. pp. 29-38.
tually zero wear can be obtained in both lubricated and dry 12 Rabino'wicz, E.. "Boundary Lubrication of Titanium.- Proc Fifthsliding. Whorld Pelt. Congr.. Vol. 6. Sect. VI-Paper 2.11 1958. pp 319-332.
13 Bar. S.. Ramalingam. S.. and Winer, W. 0.. "Tribological Experience5 Conclusions iih Hard Coats on Soft Metallic Substrates." Wear. Vol. 60. 1v80. pp
4 13-419.In light of the experimental and analytical results of this 14 RamaLingami. S., and Winer. W. 0.. "Reactiv~ely Sputter'ed TiN Coatingswork the following conclusions regarding the role of hard for Tribologicall Applications," Thin Solid Films. Vol. 73. 1980, pp 2'6" -:'S
laesin lubricated and dry sliding can be drawn: 15 Jamal. T..Nimmagadda. R., and Bunshah. R. F.. "Friction and Adhesivelaye rs laes uha icnrdc h ofiin f Wear of Titanium Carbide and Titanium Nitride Overlay Coatings." Thin Solid
(1) ardlayrs, uchas iNcan edue te coffiien of Films. Vol. '3. 1980. pp. 245-254.friction of both lubricated and unlubricated surfaces by 16 Komvopoulos. K., Saka. N.. and Suh. N P.. "The %lechanism of F-icminimizing plowing and plastic deformation. lion in Boundary Lubrication," ASME JotiwAsa OF TRJISOLOGY. Ofl 10-, ly5.
(2) The wear rates of the coated surfaces were virtually zero pp 5-6I" Kom~opoulos. K.. Suh. N. P.. and Saka. N tea B'unciars-when the hard layer was not deformed plastically. Lubriczaied Metal Surfaces.' Whear. Vol. 10'7, 196. pp IiF-I 12
(3) The finite element analysis and the experimental IS Timoshenko. S. P . and Goodier. 1 N.. T/,eor , of Ejasizou,r.N.rj etJ,evidence have verified that the deformation mode at the iion. Mlc~raw-Hill. New York. 1970. pp. 398-420.asperity contacts depends on the layer thickness, the inter- 19 Slindlin. R. D . "Compliance of Elast,c Bodies in Conta !.- \i\IE I','
nal of Applied Mechanics. Vol. 16. 1949. pp. 29-268facial friction, the magnitude of the surface tractions, and the 20 Smith. J. 0.. and Liu. C. K.. "Stresses Due to Tangental And "orramechanical properties (such as the modulus of elasticity and Loads on an Elastic Solid With Application to Some Conitic ',ilrr' i'rotmem'.hardness) of the hard layer in relation to those of the -\SIE Journal of.Applied Mechanics. Vol -5. 1953. pp ! -. Itsubstrate. 21 Hamilton. G. M.. and Goodman. L E . -The 'Sires% Field k cei~cJ 1,
(4) Rupture and removal of the protective hard layer was Circular Sliding Contact." ASNIE Journal of A4ppliedi W, t,,,. 1.' 01 11Q66. pp 1-1-3'6
found to result in high friction, severe damage, and delamina- 22 Hamilion. (., M. . "Explicit Equations for the Sire-r.' Beneauth a '.,d~nption of the sliding surfaces. Spherical Contact. P'nic. insin. 'dech. Entry % 'ol 19-c. . 'sr I"
'? Sackfield. A . ndl Hills. D A.. 'Some L seful Result, in- t j-_iiHertz Contact Proitlem." Journal of Sirain 4nalysts. \.ol I-. :.it ,Acknowledgments10-0
The work presented in this paper was sponsored by the Of' 24 Sackfield. anmd Hills. D .'Sm Useful Results in the Tasntent.ailsficeof ava Resarc uner Cntrct 0001-82K-020. Loaded Hertan Contact Problem." ibid. pp 10"- 11liriceof NvalReserch nde ConractN0014-8-K-020, 25 Bryant. VI D .and Ketr. L. %I . -Rough Contact Between Elasti~alt and
The personal support and encouragement of Dr. A. W. Ruff Geomnetricaly Identical Cu.-.ed Bodies." NSME Journal of Arpplied Slet hamu, sand Dr. R. S. Miller are appreciated. %'Of 49. 192. pp 345-352
26 Johnson. K. L . -One Hundred Years at Hertz Contact.- Prw nr%tec.h Ensit . \Vol. 196. 10Z:. pp 303-8
References " Hannah. '.1.. 'Contact Sires% and Deformation in a Thin Eha't. I jcQuart Journs Weth and 4pl Vlain. % ol I%.. '1. pp ".-I t
I G~eorges. J. .and Rabinowicz. E.. "The Effect of Film Thickness on 28 sineddon. I No . Fourier Transforms, Ivc~ra%-Hill. l'Mir 14% t~i.the weair of Hard Electrodeposits. " Wear. Vol. 14. 1969. pp. 171 -ISO, 29 Barovich. D . Kingsles. S C . and Ku. T C . .5irese% an a Thin ',-r' or
2 Hintertnann. H. E.. "Adhesion. Friction and %%ear of Thin Hard Slab wsith Different Elastic Properties trom thai oi the Substrate Due .. k ip~Coatinp." War. Vol. 100, 1914. pp. 381-397. tically Distributed Load." mIn J Engnit 5s . Vol 2. 19N.. pp -'!I 2Ni
3 Spaivina. T., "Coattnp for Wear and Lubication." Thin Solid Films. 30 Ku. T C . Ktngsles. S C . and Ramsey. J, H . "Stresses in 3 Thin "lat'Vol. 53. 2978. pp. 285-300. with Different Elastic Properties from that of the Substrate Due to lOtsrtutruj
4 Sclsintimenner, W.. Walpam. W.. K~ant, I.. ansd Gil. K.. "Cuttinil Tool Normal and Shearing Forces on the Surface of the Slab." It J f Rnt 1,t,MaterialsCoated by Ceinieal Vapow Deposition." Wear. Vol. 100. 1984, pp Vol 3. 1965. pp 93-10"153-169. 31 Gupta. P K_ and Vialotiot J A., 'Contact Stresses Betwseen in Elasic
5 Su. K.-Y.. and Cook. N. H.. 'Enhancement of High Speed Steel Tool Cvltnder and a Layered Elastic Solid." kSME JoL RAst OiF I I11ft si, ,.Life by Titanium Nitride Sputter Coating.' Proc. Fifth V .m M'eialworking TtcIINOLOGV. Vol. 96. 1974. PP. 250.25"
Journal of 'ibology 4 8 At RI L 1987. Vol. 109 1231
III
Wear, 107 (1986)107- 132 107
3 WEAR OF BOUNDARY-LUBRICATED METAL SURFACES
KYRIAKOS KOMVOPOULOS, NAM P. SUH* and NANNAJI SAKA
Department of Mechanical Engineering. Massachusetts Inatitute of Technology, Cambridge,MA 02139 (U.S.A.)
(Received August 1, 1985, accepted August 20, 1985)ISummary
In the past, the friction and wear of boundary-lubricated metallicsurfaces were attributed to adhesion and shearing of lubricants. However,examination of the friction and wear of pure metals lubricated with mineraloil indicates that while the friction coefficient was typical of the valuesobtained in boundary-lubricated sliding, the predominant wear mechanismwas an abrasive-type mechanism. Scanning electron microscopy and surfaceprofilometry revealed many ploughing grooves on the surfaces. These resultsindicate that the ploughing mechanism may be the predominant factor incontrolling friction and wear of boundary-lubricated surfaces. On the basisof slip line field analysis and surface topography statistics an approximateexpression for the wear coefficient was derived. It was found that the wearcoefficient depends on the sharpness of the surface asperities (or the entrap-ped wear debris), the interfacial "friction" and the extent of the plastically3 deformed zone below the surface.
1. Introduction
Wear in boundary lubrication attracted the attention of many investiga-tors in the past and numerous reviews of lubricated wear appeared in theliterature 11 - 4). Most of the investigations, however, focused on the reduc-tion of friction and wear, and little effort was devoted to identify the primarywear mechanism or mechanisms by which boundary-lubricated surfaces wear.
Consequently, although many of the published results provide valuableinformation about the friction and wear of specific materials, a consistenttheory for boundary-lubricated wear has not been developed yet.
One of the earliest empirical relations for wear in boundary lubricationwas obtained by Burwell and Strang (51 who slid high carbon steel onhardened steel in purified hexadecane. The experimental results of theirstudy showed that the amount of wear was proportional to the distance slid£ and the normal load, and was independent of the apparent area of contact.
*Present address National Science Foundation, Washington, DC, U.S.A.
5 0043-1648186'S3.50 Elsevier SequoiaPrinted in The Netherlands
* 49
I1~Il
108I
However, for normal pressures larger than one.third of the hardness of thesofter material wear increased rapidly.
Rabinowicz [6, 71 has proposed that adhesive wear prevails even inboundary lubrication. Surface asperities were assumed to penetrate throughthe lubricant film during sliding,. forming junctions similar to those formed Iduring unlubricated sliding and resulting in wear particle formation [8]. Onthe basis of an asperity junction model for wear, Rabinowicz has shown thatthe ratio of the lubricated wear rate to the unlubricated wear rate is equal to63/2, where 6 is a non-dimensional parameter defined by Bowden et aL. (91and Bowden and Tabor [101 as 6 = Am/A, with Am and A representing themetal-metal contact area and the real area of contact respectively.
Rowe [11] suggested that wear particles in boundary lubrication areformed at the metal-metal contacts by an adhesion process similar to thatproposed by Archard for dry sliding wear- [81, and the actual normal loadacting through the metallic contacts was assumed to be equal to 6L, where Lis the total normal load. Rowe proposed that the heat of adsorption is themost critical parameter that controls the magnitude of &. He assumed that
Dr° exp -- -
U RT
where Dm is the diameter of the adsorbed molecule. U is the sliding velocity,ro is the frequency of vibration of the adsorbed molecule, E is the heat ofadsorption, R is the molar gas constant and T is the absolute temperature ofthe surface film. However, this assumption is unrealistic because it assumesthat & and hence the coefficient of friction, which is a function of d 1101, Idepend on the sliding velocity. This argument is in complete disagreementwith the experimental evidence according to which the coefficient of frictionof boundary-lubricated surfaces is independent of the sliding velocity. I
In recent years some important objections to the adhesive wearmechanism and its contribution to wear in boundary lubrication have beenraised. It has been suggested that for typical boundary-lubricated conditionsweak adhesion between the asperity junctions is expected and, therefore, Iadhesion cannot be the prevailing wear mechanism [121. Indeed, recentwork on boundary lubrication demonstrated that ploughing of the slidingsurfaces occurred at the onset of sliding and that adhesion had a secondaryeffect 1131. Furthermore, expenments conducted on steels of differentmicrostructures indicated that the hardness alone cannot be used as a measureof wear and that the microstructure has also a significant effect on the wearresistance 1141. In a recent investigation Jahanmir [151 observed that inboundary lubrication wear particles, ranging in size from 1 to 15 gm, areformed primarily by surface deformation, ploughing and delamination of thesubsurface. However, under boundary.lubricated conditions, when the surfacetractions are too small, crack propagation cannot occur. In this case, as Suh1161 has argued, the wear process due to delamination of the subsurface willbe extremely slow and the wear rate will be controlled by the rate of crack
50
113109
nucleation. Thus a wear particle will form only when a large number ofcracks have already been nucleated so that they can link up easily eventhough the friction coefficient between boundary-lubricated surfaces is low.
Heilman et al. [17] studied the formation of wear debris underunlubricated and lubricated conditions and observed that delamination ofthe base material did not occur. It was found, however, that transfer layersbegan to develop very early, which finally delaminated to generate wearparticles. They proposed that liquid lubricants can reduce wear by dispersingand separating small wear particles before they can accumulate to formtransfer layers which may later delaminate forming large wear debris. Underboundary-lubricated conditions, however, the lubricant film is only a fewmolecules thick and thus dispersion of the wear debris is clearly impossible.
In general, under boundary-lubricated conditions the coefficient offriction assumes values between 0.1 and 0,2 and the wear coefficient is in therange 10-6 _ 10 - 3 . The conventional approach taken for lubricated sliding isthat the friction force arises predominantly from adhesion between theasperity contacts and shearing of the lubricant film. However, the formationof surface ploughing grooves cannot be explained on the basis of thesetheoretical models. Moreover, a functional relation between the wear coeffi-cient and some important parameters, such as the "interfacial" frictionconditions and the sharpness of the surface asperities and wear debris, was
not obtained. It was assumed instead that wear occurs in a manner similar tothat in dry sliding and on the basis of that assumption empirical relations forthe wear coefficient in lubricated sliding were derived.
The purpose of this study therefore is to investigate the primary wearmechanism under boundary-lubricated conditions and to explain it in thelight of the experimental results. On the basis of the experimental evidencefor the predominant wear mechanism a slip line field analysis is performedaand an expression for the wear coefficient is derived.
12. Experimental procedures
2.1. Materials and lubricantThree metals were used in this investigation: aluminum (99.999% pure),
oxygen-free high conductivity (OFHC) copper (99.999% pure) and chromium125 pm thick electroplated on AISI 1095 steel. The choice of the materialswas on the basis of their large range in hardness. Table 1 shows the experi-mental materials, their hardnesses before and after annealing and the anneal-ing temperatures. In order to avoid complications associated with additive-laden lubricants, a relatively inert additive-free mineral oil was used in theexperiments. The density of the mineral oil at 298 K is 0.89 g cm - 3 and theflash point temperature is 457 K. The viscosity at 310 K is 74 cSt and at
372 K it is 11 cSt.
5
II
110
TABLE 1
Experimental materials
Material Hardness (MPa) Temperature of
Before annealing After annealin annealg(Kin Ar for I h
Al (99.999% pure) 294 ± 52 186 ± 16 673OFHC Cu (99.999% pure) 1363 ± 53 510 ± 21 873Cr (125/um thick, electroplated 6590 ± 284on AISI 1095 steel6)
'Hardness, 3500 ± 451 MPa.
2.2. Specimen preparation 1
Cold-worked aluminum, copper and AISI 1095 steel rods 2.54 cm and0.635 cm in diameter were used to prepare the specimens. Disks (2.54 cm indiameter and of about the same thickness) and pins (0.635 cm in diameterwith hemispherical tips of the same diameter) were cut and machined from 1the cold-worked rods. Before annealing, the aluminum disks were polishedwith 600 grit SiC abrasive paper and the copper disks with 240, 320 and 600grit SiC. The annealed aluminum and copper specimens were polished with l0.3 pm ot-A120 3 and 0.05/jm y-A120 3 to obtain a very smooth surface finish.The specimens finished with alumina were cleaned with warm water andsoap, rinsed with distilled water and methanol, dried in air and stored in adesiccator with Ca2 504 at room temperature to protect them from watervapor.
The steel specimens were polished with an abrasive cloth and mineraloil to obtain a smooth surface. Then they were cleaned with warm water and Isoap, rinsed with methanol and electroplated with chromium, approximately
125 pm thick. The electroplated chromium disks were polished with 320and 600 grit SiC abrasive paper and 0.3 jm C-A120 3 , while the pins werepolished with 0.3 pm a-A 20 3 . All the specimens were then cleaned, as forthe aluminum and copper specimens, and stored in a desiccator with Ca 2504at room temperature. 32.3. Experimental apparatus
Lubricated sliding tests were conducted in air at room temperatureusing a pin-on-disk tester (Fig. 1). The disks were mounted on a metal platewhich was rotated at 4.5 rad s- 1(43 rev mn - 1) and the pin was held stationaryin a holder attached to a strain ring. A Plexiglas container was used as areservoir for the lubricant. At the end of each experiment the loose weardebris and contaminated oil were removed with warm water and methanol.A normal load of 2 N (204 gf) was used for all the experiments, while thesliding velocity was varied betwp-n 0.6 and 4.3 cm s-1. These experimentalconditions were chosen so that iydrodynamic effects due to light loads I
52
III 111I
II
I Fig. 1. Experimental apparatus.
3 TABLE 2
Test conditions
Load 2 N (204 gf)Angular speed 4.5 rad s - 1Tangential speed 0.6 - 4.3 cm s-1
Distance slid 0.03 - 100 mLubricant Mineral oilTemperature f, 294 KRelative humidity 20%- 30%
I and/or high sliding speeds did not occur. The experimental conditions arelisted in Table 2. The pin and disk specimens used in each test were identical.
2.4. Wear measurementsBecause of the very low wear rates, a surface profilometer was used to
trace the profile of the worn surfaces in a direction normal to the slidingdirection. In order to obtain accurate estimates for the wear volume of thedisk specimens at least four profiles, depending on the scatter, were obtainedat different locations. The wear volume of each pin was calculated from thediameter of the circular (approximately) worn surface measured with anoptical microscope and the radius of the hemispherical tips. The experimentalfriction and wear data were assumed to follow a normal distribution.
Special attention was devoted to the changes in the surface topography5 with sliding distance. Thus micrographs of several wear tracks were obtained
II 5
112
for different sliding distances using a scanning electron microscope. Anenergy-dispersive X-ray analyzer was used after each experiment withchromium to check whether the AISI 1095 steel subsurface was exposedduring the wear test.
3. Experimental results
Figure 2 shows some typical profiles of aluminum worn surfaces forvarious sliding distances. It can be seen that the surface roughness and thewidth of the wear track increase with sliding distance until a steady state isreached and then they remain almost constant. In Fig. 3 some characteristicsurface profiles of copper surfaces are shown. Again, the depth of the weargrooves and the width of the wear track increase with sliding. However, thedepth and width of the wear grooves are much smaller than those on thealuminum surfaces. Profiles of worn chromium surfaces are shown in Fig. 4.
(a) "
(b)
IA
A -
(C)
/V\\/ f'\.
(d)
Fig. 2. Surface profiles of the aluminum disk specimens for various sliding distances(lubricated experiment; normal load, 2 N): (a) 0.22 m (10 rev); (b) 7.5 m (260 rev);(c)60 m (1935 rev); (d) 78 m (2064 rev).
54
I A
II 113
(a) (b)
c(d)
I ALMFig. 3. Surface profiles of the copper disk specimens for various sliding distances (lubricatedexperiment; normal load. 2N) 2 Na) 0.37 m (10 rev), (b) 3 m (205 rev); (c) 17.5 m (963 rev);
(d) 22.5 m (1862 rev); (e) 44 m (950 rev).
(c) (d)
| m
Fig. 4. Surface profiles of the chromium disk specimens for various sliding distances
(lubricated experiment; normal load, 2 N): (a) 0.37 mn (10 rev); (b) 16 mn (440 rev); (c)I 30.5 in (1080 rev); (d) 36.2 in (896 rev); (e) 54.4 in (1920 rev).
It can be seen that although the surface topography of the chromium surfaceschanges with the distance slid, it does not undergo drastic transitions such asthe aluminum and copper surfaces do. Moreover, the depth of the weargrooves and the width of the wear track appear to be much smaller. Thesurface profiles shown in Figs. 2 - 4 demonstrate that the depth and thewidth of the wear grooves decrease as the hardness of the surfaces increases.
Table 3 lists the steady state coefficients of friction, the calculatedtotal wear rates and the total wear coefficients, together with their standarddeviations, for the materials tested. Aluminum has a coefficient of frictionof 0.2 and a wear rate of the order of 10-8 cm 3 cm-, while copper and
I
I,, , 55II
114 5TABLE 3
Experimental resultsI
Material Coefficient Wear rate Wear coefficientof friction (cm cm-) Based on annealed Based on cold-state) hardness worked hardnesb
Pure Al 0.20 ± 0.02 (4.3 ± 2.1) x 10- 8 (1.2 ± 0.6)x 10-3 (2.3 ± 1.2) x 10 - 3
OFHC Cu 0.17 ± 0.02 (2.0 ± 1.1)x 10- 9 (1.5 ± 0.9)x 10- 4 (4.0 ± 2.4)x 10 - 6Electroplated 0.15 ± 0.01 (6.6 ± 2.2)x 10-10 (6.5 ± 2.1)x10- 4 (8.7 ± 2.8)x10-4
Cr
'Normal load, 2 N.bHardneses: Al, 343 MPa; Cu, 1372 MPa, Cr, 8820 MPa. 5chromium have lower friction coefficients, 0.17 and 0.15 respectively, andwear rates of the order of 10 - 9 cm 3 cm - ' and 10-10 cm3 cm - 1 respectively.The coefficients of friction are similar to those reported in the literature. IThe results also indicate that the hardness of the sliding surfaces plays animportant role in boundary lubrication as well.
Although all the surfaces were highly polished and carefully cleanedbefore each experiment, ploughing grooves and wear debris formed on thesurfaces. More grooves and wear debris were formed as sliding continued.The wear particles either became loose and were removed by the lubricantor adhered to one of the surfaces, ploughing the counterface as they slid on Ieach other. Figure 5(a) and its higher magnification (Fig. 5(b)) show the
material which adhered on a chromium pin after sliding on a chromium diskfor 0.37 -m. The wear debris entrapped at the interface is under a triaxialstate of stress and thus can plough and cut the surfaces, forming microchipsand new wear debris. Accordingly, the analysis presented later is based on I'~II
II
Fig. 5. (a) Worn surface of a chromium pin (lubricated test; normal load, 2 N; distance
slid, 0.37 m (10 rev)). (b) Higher magnification of (a). The arows show the sliding direc-tion.
5I
56 3
II1 115
I s
Ii
II.
3 10am50JAM
Fig. 6. Wear tracks of the aluminum surfaces (lubricated experiment; normal load, 2 N;3 distance slid, 0.22 m (10 rev)): (a) disk; (b) pin.
the shape of the wear grooves formed, assuming that the wear particles arerigid in contrast with the plastically deforming surfaces. Some characteristicmicrographs of aluminum, copper and chromium surfaces, obtained after10 rev of sliding, are shown in Figs. 6 - 8.
Figure 6 shows the surface topography of aluminum specimens after10 rev (0.22 m). Numerous ploughing grooves and wear debris can beobserved, especially on the disk surface, and extensive plastic deformation ofthe pin surface. Figure 7 shows wear tracks of copper specimens obtainedafter 10 rev (0.4 m). As for aluminum, wear grooves and wear debris haveformed on both surfaces. (Figure 7(b) clearly shows two large wear particleswhich adhered to the pin surface.) Ploughing grooves and wear particleformation can be observed on chromium surfaces after 10 rev (0.37 m) ofsliding (Fig. 8). However, the width of the wear track and the number ofploughing grooves are significantly less than those of aluminum and coppersurfaces (Figs. 6 and 7). A comparison of the worn surfaces after 10 rev
II[5
116
Fig. 7. Wear tracks of the copper surfaces (lubricated experiment; normal load, 2 N;distance slid, 0.4 m (10 rev)): (a) disk; (b) pin.
aI
Fig. 8. Wear tracks of the chromium surfaces (lubricated experiment; normal load, 2 N;distance slid, 0.37 m (10 rev)): (a) disk; (b) pin.
58
3 117
I
I-..
3 100 urn
Fig. 9. Wear tracks of the aluminum surfaces (lubricated experiment; normal load, 2 N.distance slid, 83.6 m (2150 rev)): (a) disk; (b) pin.
shows that plastic deformation and wear groove formation on the surfacescan be reduced if the hardness of the sliding pair is increased.
Similar observations were made for the surface topographies after longsliding distances. For instance, Figs. 9 and 10 show the worn surfaces ofaluminum and chromium specimens after 2150 rev (83.6 m) and 1900 rev(85.2 m) respectively. It is clear that plastic deformation and wear grooveand wear particle formation occurred on all the surfaces, although the hard-ness of the materials was substantially different.
The experimental results of this investigation illustrate the role of thewear debris in boundary lubrication. The formation of ploughing grooves onhighly polished and well-cleaned surfaces immediately after sliding is initiatedcan be explained only from the ploughing action of the entrapped weardebris. When sliding commences some of the asperity junctions deformplastically and eventually fracture, producing small wear particles and thus
initiating an abrasive-type wear mechanism. The wear particles adhere to orindent one of the sliding surfaces and, as a result, ploughing or microcuttingof the opposite surface occurs. The observed ploughing grooves and themicrocutting action of the wear debris demonstrate that under boundary-
5
118 1
Ul u-I I
Fig. 10. Wear tracks of the chromium surfaces (lubricated experiment; normal load, 2 N;distance slid, 85.2 m (1900 rev)): (a) disk; (b) pin.
lubricated conditions the primary wear mechanism is an abrasive-type wear Imechanism and that adhesion has a secondary contribution to the total wear.
4. Analysis and discussion of the wear mechanismI
The experimental work of this investigation clearly demonstrates theimportant role of the wear debris in the wear of boundary-lubricated surfaces.During sliding, wear particles are formed some of which become entrapped Iat the sliding interface while the rest are removed by the lubricant. Theentrapped wear debris can plough and cut the surfaces as they slide on eachother, resulting in groove and microchip formation. Ploughing and micro-cutting of the surfaces can also result from asperities formed duringfragmentation of the ridges along the ploughing grooves. In order to studythe ploughing action of the wear particles (or surface asperities) in boundarylubrication it may be assumed that a plane strain slip line solution approxi-mates the ploughing situation fairly well.
It should be noted that there are similarities of metal flow betweengrinding and abrasion during sliding. Thus the slip line fields proposed forgrinding may be adopted for analyzing abrasion as well. A great deal ofeffort has been devoted in the past to obtain analytical solutions for suchcomplex problems as those in machining operations. However, most of theslip line analyses were performed in an attempt to obtain analytical solutions Iprimarily for machining operations (e.g. cutting, drawing, extrusion and
60
I 1
I 119
grinding) and very little was done to analyze the abrasion of metals in slidingwear.On the basis of the ideal plastic behavior of an isotropic materialdeforming in plane strain, Lortz [ 181 developed a slip line model for plough.ing and cutting conditions. The proposed model accounts for the formationof a dead zone between the plastically deformed material and the penetrat-ing spherical indenter, the interfacial friction conditions and the transitionfrom ploughing to cutting conditions with the formation of a quasi-continuouschip. Although the suggested model seems to be in fair qualitative agreementwith the experimental observations (e.g. dead zone and chip formation andthe shape of the plastic zone) analytical solutions were not obtained andthus comparison with other models and available experimental results isimpossible. However, Lortz's analysis sheds much light on the most essentialcharacteristics that a slip line field appropriate for ploughing and cuttingconditions must account for.
Rowe and Wetton [ 19] developed a model for grinding based on theslip line approach, which can also be used to analyze abrasion in sliding ifmodified to account for interfacial friction. The model predicts a transitionfrom continuous to discontinuous chip formation when the absolutevalue of the negative rake angle increases up to a critical value. On thebasis of the assumed slip line field they derived a semi-empirical expressionfor the rake angle as a function of the depth of penetration and the heightof the material displaced ahead of the truncated wedge. Good correlationwas found between the theoretical magnitudes of the critical rake angle andthe experimental results obtained from experiments conducted with large-scale model grits sliding on plasticine.
Several slip line solutions for two-dimensional machining were alsoproposed and discussed by Kudo [20) and some characteristic phenomenaobserved in actual machining were explained quantitatively under theassumption of a rigid perfectly plastic model. Although most of the proposedmodels may be appropriate for cutting conditions with positive rake angletools, the discussed slip line fields for machining with negative rake angles,involving a built-up edge (dead zone) and a pre-pilp-up (ridge), were foundto be kinematically incompatible (i.e. all the velocity boundary conditionswere not satisfied simultaneously). Consequently, the accuracy of thesuggested slip line models for negative rake angles appears to be fortuitous.
Recently, Challen and Oxley (211 analyzed the friction and wearphenomena on the basis of three different slip line fields, namely the rubbing,wear and cutting models. The rubbing model, however, cannot be employedfor analyzing wear because it does not account for material removal. Thewear model was proposed for the wear of relatively smooth surfaces but theproposed slip line field does not satisfy the kinematic constraints on theproblem. For rough surfaces the cutting model was proposed. This model iskinematically admissible but it assumes that plastic deformation takes placeabruptly at a single shear plane and, moreover, it does not account for the3 plastically deformed material sufficiently ahead of and below the shear plane.
I3 61l iIII
120
Ae
Soft 6 F
DI
IjI(a) 3.
(b) UD
Fig. 11. (a) Slip line field and (b) hodograph.
The slip line model used in this paper is shown in Fig. 11 and is basedon the work of Abebe and Appl [22]. Figure 11(a) shows a hard asperity(or wear particle) sliding and cutting a softer material which deformsplastically resulting in microchip formation. The proposed slip line fieldis kinematically compatible (Fig. 11(b)).
For the geometry shown in Fig. 11(a) the volume wear rate V can bewritten as
V= tUAD (1)
where t is the microchip thickness and UAB is the relative velocity betweenthe microchip and the hard asperity.
The microchip thickness t is given by
t - AIsin(4 + 7
or
t AB2 12 cos 7, sin( 4 + 11i) (2)
Substituting into eqn. (2) the expression for AB, as given by the first ofeqns. (A7), the thickness t may be rewritten as (Appendix A)
I62
II
I cos 1t co s(1 2 + 0 /2 ) sin ( 3 + A - a) 12 1
t sin 0 sin(P - - 0/2) (3)
where the angles 0, A and 0 are given by eqns. (A9), (A10) and (A13)respectively in Appendix A.
Volume conservation requires that the velocity normal to IB must bethe same in both fields AIB and JIB. Thus
i Cos 172
COS ?71
or
S=UJ cos(7, - 0/2) cos i7orm = Ujcos( 2 + 0/2) cos 77
or
I U B sin( 7 + 0- (4)
UAB = U cos7 11 cos(772 + 0/2)w Ahr = UAB, and TjB and IJ are the velocities in JIB on the i3 lines
IB and IJ respectively.Substituting eqns. (3) and (4) into eqn. (1), the volume wear rate V can
be expressed asIV = JC sin(771 + 0- Of) cos(772 - 0/2) sin(O + ,A -a) U (5)
sin 0 sino - a - 0/2)
Using eqn. (5) for the volume wear rate, the wear coefficient K can bewritten as
3HV 3H sin(Th + 0 - a) cos(12 - 0/2) sin( + A - a) (6)K=- - =JC -LS L sin 0 sin(3 - a - 0/2)
Substituting eqn. (A8) into eqn. (6) and assuming that H = 6k, where kis the shear strength, the wear coefficient can be expressed as
18sinf + 0-)cos(? 2 -0/2) I2 /2 cos(1 2 + 0/2) cos(ir/4 + 77 -a)s = n18 s sin 0
- {1 + sin(22)} sin( '- 2o - 0) + sin(/2)
- {2- cos(2 2 )j cos(P -2a - -- +
sin(-a -0/2)+ 1(1 + 20 + 20) sin(P +A- 2a) + cos( +A- 2a - 2173)}I
sin(P + A - a)
3(7)
II* 63
122
It can be seen that the wear coefficient as given by eqn. (7) is a functionof the semi-asperity angle a, the shape of the plastic zone and the interfacialshear strength sj, along AB, BJ and JC, which is a function of the "friction"angles il (eqn. (A2)).
10~
_ -
U.w 01-0
001-
0001
45 50 155 60 615 7C 75 80 85 90(a) a aeQg
1001,6 T~
U,.o. .I,
01U
001 -
0 5 50 5 60 65 70 75 so 05 90(b) a (doq
Fig. 12. Slip line solutions for the wear coefficient as a function of the semi-asperity anglea for different interfacial friction conditions: (a) maximum; (b) minimum.
64
UI3 123
Figures 12(a) and 12(b) show the maximum and minimum magnitudesof the wear coefficient as a function of the angle a when the same frictionconditions prevail along the boundaries AB, BJ and JC, i.e. i = 172 = 3. Thefigure shows that the wear coefficient decreases when the angle a increases.In the case of very sharp asperities (or wear particles) the wear coefficientassumes values of the order of unity while in the case of very blunt asperitiesit reduces significantly to small magnitudes of the order of 10- - 10-4.Theresults also illustrate the importance of the interfacial shear strength s on themagnitude of the wear coefficient. For a given semi-asperity angle a the wearcoefficient increases when the interfacial shear strength decreases and obtainsa maximum in the case of "frictionless" interfacial conditions (i.e. whens = 0). (Incidentally, this provides important insight into abrasive machining:sharp abrasives and lubricants should be used to. maximize the materialremoval rate.) In the particular case of "sticking" at the interface, i.e. whens/k = 1, the slip line shown in Fig. 11 is not valid. Under boundary-lubricatedconditions, however, sticking is unlikely to occur and the ratio s/k assumesvalues of about 0.1.
Solutions for the wear coefficient may be obtained as long as thegeometric conditions, eqns. (A10) - (A14), are satisfied. The broken curvesin Figs. 12(a) and 12(b) indicate the limit of the solutions obtained from theproposed slip line field (Fig. 11). Outside the broken curves different slipline fields must be generated. However, under lubricated sliding cunditions,the curves for s/k = 0, 0.1, 0.2 and 0.3 may be the appropriate curves. Underthese interfacial friction conditions solutions for the wear coefficient havebeen obtained for a large range of the semi-asperity angles a.
Measurements based on the topography of the worn surfaces indicatedlarge variations in the magnitude of the semi-included angle of the surfacegrooves. This implies that the sharpness of the surface asperities and theentrapped wear debris in general varies over a large range of values. Becausethe magnitude of the wear coefficient is a strong function of a, as shown inFigs. 12(a) and 12(b), the calculation of wear coefficients on the basis of themean value of a may not give a realistic estimate. Sharp asperities and acicular
wear particles contribute more to wear than do shallow asperities and smoothwear particles. Figure 13 shows the percentage of the grooves with semi-included angles less than a as a function of a. The data points correspond tomeasurements taken from lubricated worn surfaces obtained from experi-ments conducted for various sliding distances, but always after the steadystate coefficient of friction was reached. It can be seen that the cumulativedistribution is different for the materials tested and that the mean value ofa shifts towards a = 90° as the material hardness is increased. It is necessary,therefore, that eqn. (7) be modified accordingly to account for the widevariation in a.
Moreover, the analysis presented so far was based on a two-dimensionalslip line field analysis. Although this type of analysis is appropriate forpredicting forces accurately, it overestimates the volume wear rate becauseit assumes that all the material that has been ploughed is removed completely.
I* 6
124
100-Z" 0
zW
20" -
01so 55 s0 65 70 75 80 85 90
a (degFig. 13. The percentage of grooves with a semi-included angle leg than 0 as a functionof a: 0, pure aluminum; A, OFHC copper;*, electroplated chromium.
It is well known, however, that only a small proportion of the ploughedmaterial is removed and that the rest deforms plastically resulting in ridgeformation. Goddard et at. (231 conducted dry sliding experiments of variousmetals on abrasive papers and observed that less than 10% of the groovevolume was removed as wear debris. Avient et a!. [24] conducted similarexperiments and concluded that most of the energy was expended in plough-ing and only 10% of the groove volume was removed completely from thesurfaces. Stroud and Wilman [251 slid silver on emery paper (mean particlediameter, 5 /&m) and estimated the proportion of the total groove volumeremoved to be about 10%. Experiments conducted by Sin et at. [261 withconical diamond tools sliding on AISI 1095 steel showed that the ratio ofthe volume removed to the calculated groove volume approaches values wellbelow 0.1 for attack angles less than 20*, i.e. for a > 700 (Fig. 14). Thus asecond modification of the derived expression for the wear coefficient isappropriate to account for the proportion of the groove volume removed.
It can be assumed that the formation of grooves of semi-included anglea is due to the ploughing action of surface asperities (and/or wear particles)with semi-asperity angles a. The normal load dL carried by the asperities ofthe same angle a is a fraction of the total normal load L and can be expressedas
dL - Lf(a) da (8)
where f(a) represents the probability density function of asperities withsemi-asperity angle a and thus satisfies the following relation:
66
II
125
0
04 .
060 4
E 0.2
mO
I5 25 35 45 55Atrack A~qe dOlreS
Fig. 14. Ratio of the groove volume removed to the calculated groove volume as a functionof the attack angle for AISI 1095 steel (26] (attack angle, 90 - a).
f f(a)dCa=1
The theoretical volume wear rate dVh can be expressed asIdLdVt, = Kth(a, slk, 0 .. ) S (9)
3H
where Kth(a, s/k, 0, ... ) represents the theoretical wear coefficient given byeqn. (7).
Substitution of eqn. (8) into eqn. (9) yiedsLS
dVth = Kth(a, s/k, 0, ... ) f(a) da (10)
If dVa is the actual volume wear rate obtained from grooves with the samesemi-included angle a, then
dV, = t(a) dVb (11)
where e(a) represents the proportion of the theoretical volume that actuallyis removed.
If eqns. (10) and (11) are combined the following expression for theactual volume wear rate dV is obtained:
dV = t(a)Kth(a, slk, 0... ) - f(a) da (12)
Integration of eqn. (12) produces the total actual wear volume V.
IV. V 3- f t ( o)Kh(a. s/k, 9,. .. )f(a) do (13)3H0
67
I
126
Hence, the actual wear coefficient K. can be obtained from eqn. (13)by using K, = V.(3HILS) as
i/2
K1 = f t(a)Kth(ca, s/k,O,...)f(o)da (14)0
The probability density function f(a) can be expressed in terms of thefraction AN/Aa, which represents the asperities of semi-asperity angle a inthe range Aa, and the total number NT of asperities as follows:
S dN(a)I
1 dN(a)
NT da 31 AN(c)
NT(15)NT AaI
Thus, using eqns. (14) and (15), the actual wear coefficient K. can bewritten as
K, f 2(u)Kth(c(, s/k, 0, ... ) 1 A- dc, (16)0NT A
Table 4 lists the experimental wear coefficients for the tested materials Utogether with the theoretical wear coefficients obtained by numericallyintegrating eqn. (16). Since appreciable work hardening occurs during thefirst few revolutions of sliding, the fully cold-worked hardness was used in Ithe calculations of the experimental wear coefficients. The minimum andmaximum values of the theoretical wear coefficient Kth used in eqn. (16)
TABLE 4 1Experimental and theoretical wear coefficients
Material Experimental wear Theoretical wear Theoretical wear Icoefficient a coefficientb coefficientc
Minimum Maximum Minimum Maximum
Pure Al (2.3 ± 1.2) x I0 - 3 4.8 x 10- 2 5.5 x 10- 7.7 x 1O- 7.3 x 10 - 2
OFHC Cu (4.0 ± 2.4)x 10 - 4 9.7 x I0 - 3 1.6 x 10 - 2 9.2 x 10 - 1.5 x I0 - 4
Electroplated (8.7 ± 2.8) x 10 - 4 3.3 x 10 - 3 5.5 X 10 - 2 2.6 x 10 - 5 5.1 x 10 - 4
Cr
Based on the cold-worked hardness.bFor sek a 0.1 and t(a) - 1.
eFor j/k 0.1 and 0.005 - e(a) w 0.3. IIU
68 I
127
3 were obtained for the case that sik = 0.1, which is a reasonable approxima-tion for boundary-lubricated surfaces. The theoretical wear coefficientslisted in Table 4 were obtained for t(a) = 1 and for t{a) values in the range0.005 - 0.3, obtained from Fig. 14 by extrapolation. The agreement betweenexperimental and thmoretical wear coefficients is reasonably close.
Figures 12 and 13 clearly show that the wear of boundary-lubricatedsurfaces can be reduced significantly if hard materials are used. Coating thesliding surfaces with hard layers (e.g. oxides and nitrides) may preventploughing, thus minimizing the abrasive-type wear mechanism. Indeed,experimental work in progress with titanium nitride (TiN) layers of differentthicknesses deposited onto pure titanium and AISI 1095 steel has shownthat the wear of the lubricated surfaces was virtually insignificant. Underthese conditions most of the solid-solid contacts deform only elastically and3 the wear is practically zero.
5. Conclusions
On the basis of the experimental results and the plane strain slip lineanalysis of the present work the following conclusions may be drawnregarding the wear of boundary-lubricated metal surfaces.
(1) During lubricated sliding, wear particles are formed which becomeentrapped at the interface resulting in ploughing and microcutting of thesurfaces.
(2) The magnitude of the experimental coefficient of friction obtainedunder these ploughing conditions was between 0.1 and 0.2, which is typicalof boundary-lubricated sliding.
(3) The predominant steady state mechanism of material removal isI an abrasive-type wear mechanism.(4) On the basis of the slip line analysis and the statistics of the surface
topography, an expression for the wear coefficient was obtained. The wearcoefficient was found to be a function of the sharpness of the surfaceasperities and the entrapped wear debris, the interfacial shear strength(lubricant effect) and the shape of the plastic zone.
1 Acknowledgments
The work presented in this paper was sponsored by the Office of NavalResearch under Contract N00014-82-K-0520. The authors are grateful toDr. A. W. Ruff and Dr. R. S. Miller for their personal support and encourage-ment.
References
i 1 E. Rabinowicz, Friction and Wear of Materials. Wiley, New York. 1965, pp. 198 - 220.
6* 6
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2 M. B. Peterson, Mechanisms of wear. In F. F. Ling, E. E. Klaus and R. S. Fein (eds.),Boundary Lubrication: An Appraisal of World Literature, American Society ofMechanical Engineers, New York, 1969, pp. 25 -34. I
3 W. E. Campbell, Boundary lubrication. In F. F. Ling, E. E. Klaus and R. S. Fein (eds.),
Boundary Lubrication: An Appraisal of World Literature, American Society ofMechanical Engineers, New York, 1969, pp. 87 - 117.
4 C. N. Rowe, Lubricated wear. In.E. R. Booser (ed.), CRC Handbook of Lubrication, ITheory and Practice of Tribology, Vol. II, Theory and Design, CRC Press, BocaRaton, FL, 1984, pp. 209 -225.
5 J. T. Burwell and C. D. Strang, On the empirical law of adhesive wear, J. Appl. Phys.,23 (1952) 18 - 28.
6 E. Rabinowicz, The relation between friction and wear for boundary-lubricatedsurfaces, Proc. Phys. Soc. London, Sect. B, 68 (1955) 603 - 608.
7 E. Rabinowicz, Friction and Wear of Materials, Wiley, New York, 1965, Section 8.3.8 J. F. Archard, Contact and rubbing of flat surfaces, J. Appl. Phys., 24 (1953) 981 -988.9 F. P. Bowden, J. N. Gregory and D. Tabor, Lubrication of metal surfaces by fatty
acids, Nature (London), 156 (1945)97 - 101.10 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Clarendon,
Oxford, 1958. pp. 219 -227.11 C. N. Rowe, Some aspects of the heat of adsorption in the function of a boundary
lubricant, ASLE Trans., 9 (1966) 101 - 111.12 S. Jahanmir, On the wear mechanisms and the wear equations. In N. P. Sub and
N. Saka (eds.), Fundamentals of Tribology, Massachusetts Institute of TechnologyPress, Cambridge, MA, 1980, pp. 455 - 467.
13 K. Komvopoulos, N. Saka and N. P. Suh, The mechanism of friction in boundarylubrication, J. Tribo., 107 (1985) 452 - 462.
14 S. Jahanmir, Wear of AISI 4340 steel under boundary lubrication. In S. K. Rhee,A. W. Ruff and K. C. Ludema (eds.), Proc. Int. Conf. on Wear of Materials. San UFrancisco, CA. March 30 . April 1, 1981, American Society of Mechanical Engineers,
New York, 1981, pp. 648 -655.15 S. Jahanmir, Wear mechanisms of boundary-lubricated surfaces, Wear 73 (1981) 169 -
184.16 N. P. Suh, Wear mechanisms: an assessment of the state of knowledge. In N. P. Suh
and N. Saka (eds.), Fundamentals of Tribology, Massachusetts Institute of TechnologyPress, Cambridge, MA, 1980, pp. 443 - 453.
17 P. Heilmann, J. Don, T. C. Sun, D. A. Rigney and W. A. Glaeser, Sliding wear andtransfer, Wear, 91 (1983) 171 - 190.
18 W. Lortz, A model of the cutting mechanism in grinding, Wear, 53 (1979) 115 - 128.19 G. W. Rowe and A. G. Wetton, Theoretical considerations in the grinding of metals,
J. Inst. Met., 97(1969) 193 -200.20 H. Kudo, Some new slip-line solutions for two-dimensional steady-state machining,
Int. J. Mech. Sci., 7 (1965) 43 - 55.21 J. M. Challen and P. L. B. Oxley, An explanation of the different regimes of friction
and wear using asperity deformation models, Wear, 53 (1979) 229 - 243.22 M. Abebe and F. C. Appl, A slip-line solution for negative rake angle cutting, Proc.
9th North Am. Manufacturing Research Con f., Pennsylvania State University, Univer-sity Park, PA, May 19 - 22, 1981, Society of Manufacturing Engineers, Dearborn, MI,1981, pp. 341 - 348.
23 J. Goddard, H. J. Harker and H. Wilman, A throry of the abrasion of solids such asmetals, Nature (London), 184 (1959) 333 -335.
24 B. W. E. Avient, J. Goddard and H. Wilman, An experimental study of friction andwear during abrasion of metals, Proc. R. Soc. London, Ser. A, 258 (1960) 159 -180.
25 M. F. Stroud and H. Wilman, The proportion of the groove volume removed as wearin abrasion of metals, Br. J. Appl. Phys.. 13 (1962) 173 - 178.
26 H. Sin, N. Saks and N. P. Suh, Abrasive wear mechanisms and the grit size effect,Wear, 55 (1979) 163 - 190.
70
III 129
Appendix A
A. 1. A slip line analysis for ploughingFigure 11 shows a slip line field, which is based on the work of Abebe
and Appl [Al], with the corresponding velocity field (hodograph) for a hardasperity (or wear particle) cutting a softer surface which is moving with arelative velocity U. Along each a and 3 line the equilibrium and yield condi-tions are satisfied. The hydrostatic pressure p and the shear angle 4) are given
for each slip line from Henky's equations [A2, A3J
p+2k4) C, (a line)
and (AI)
3 p- 2 C2 (3line)
where C1 and C2 are constants. On the basis of eqns. (Al) and Mohr's circlethe stresses in each field can be obtained. The triangular fields AIB, IGH andJDC and the rectangular field IFEJ consist of straight a and ( lines; thereforethe hydrostatic pressure remains constant in each of these fields. Howiver,the sectors GIF, BIK and EJD and the field KBJ are networks of straight andcircular orthogonal a and ( lines; therefore the hydrostatic pressure isconstant only along the same radial line.
Since there are no normal or tangential stresses at the surfaces HI andIA (stress-free surfaces), the a and ( lines meet these surfaces at 45'. Theangles T1, 12 and 73 that the a and ( lines make with the interface ABJCdepend on the interfacial shear strength si. Hence, from Mohr's circle, thefollowing relations are derived:
s = k cos(2j)
or
?7, =- cos - ( j = 1, 2, 3 (A2)
where 1, 2 and 3 represent the boundaries AB, BJ and JC respectively.From the given boundary conditions, i.e. stress-free surfaces and eqn.
(A2), and from Henky's equations and Mohr's circle, the normal andtangential stresses, a,, and a, respectively, along the interface ABJC areas follows: along interface AB,
oa=k{1 + sin(27?1)". oa k cos(277 ) (A3)
along interface BJ,
4' =f fi 1 + 2U + sin(21?2)j1 o ffi k cos(2772 ) (A4)
and along interface JC,
oJc= k{1 + 20 + 20 + sin(2r73)' J c = -k cos(2r73) (A5)
I3 7
II
130
The vertical and horizontal forces can be expressed in terms of the slip Iline angles, the semi-asperity angle a and the interfacial "friction" conditionsgiven by eqn. (A2). The normal force L is given by
AB(o a sin a +ucosa)+
+OBf {oajsin(i7 2 - 77 + a- 4) +,og cos(7?- 7, + a-- )) dJ +
(A6)The lengths of AB and OB are related to the length JC through the
following trigonometric relations:
cos(77 2 + 8/2) sin(rl - + 6 + A)ABJ 2 /2 cos 0 r/4 -- rht) sjn sin0l,7 72 +612)" os(8/) sin(r -- +2 + A) (A7)
sin sn(77, -- z+ /2)Substitution of eqns. 4A3) - (A5) and (A7) into eqn. (A6) and summa-
tion gives the following expression for the normal force L:
J~I sin(__,_--__ " 2cos(7 2 + O/2)cos(ff/4+* ,--ac)AB = JC Cs--6 + 0/2) sin6 --
23,12~~~~ ~ cos(ir4-7 i i 7 -12+/2)
+ sin(2r ). sin(3 - - 0/2) + sin(O/2) 3-{2 -- cos(2n2 )} cos(-2a - I2j + (1 + 2 + 2)sin(0 + A-2a) +
+ cos(+ A-- 2a -273)) (AS)
where
ti, of 72 + ( + a (A9)At point J the summation of all the angles must be equal to 2. This
condition yields I+-2 + A -7 2 - 2 (A10)
Along the discontinuity t3 line HGFEDC the velocity must be the same.
HenceUo d I
I
I72
I
131
* or
= rderfor1 a micoc-sinto(22 sin(ir t+a - ia-2) sin f3 (All)
* and
UEF =UHG3 or
I1- 2" sin(r/4 + ci-v 1 -20) cos(fl+ - c)
In order for a microchip to form the material should flow plasticallyaround I. For this flow to happen the angles HIM, BIN and JN must be3 non-zero. From these constraints the range of 0 yieldsira 7 0< 2( +a -71and (A13)
0 < r/4
For a dead zone to form the angle BCJ must be non-zero, i.e.7r.
7- -- 73>O (A14)2These geometric conditions, i.e. eqns. (A1O) - (A14), must be satisfied
in addition to the equilibrium conditions for the slip line field shown inFig. 11(a) to be valid. The relations (A13) indicate that there can be aninfinite number of solutions within the limits set by the relations. However,in the present study solutions were obtained for all the allowed values of 0,set by the relations (A13), and the maximum and minimum wear coefficientsI were obtained as a function of a and s/k.
References for Appendix AAl M. Abebe and F. C. Appl, A slip-line solution for negative rake angle cutting, Proc.
9th North Am. Manufacturing Research Conf, Pennsvlrania State Unwersity.University Park. PA. May 19 - 22. 1981. Society of Manufacturing Engineers.Dearborn, MI. 1981. pp. 341 - 348.
A2 R. Hill, The Mathematical Theory of Platicity. Oxford University Press, London,1967, pp. 128 -149.
A3 L. M. Kachanov, Fundamentals of the Theory of Plasticity, Mir, Moscow, 1974,pp. 148 - 184.
5 Appendix B: Nomenclature
C1, C2 constantsf probability density function of grooves (or asperities)H hardness
II
132
k shear strengthK, Kth theoretical wear coefficientsK. actual wear coefficientL total normal loadN number of grooves (or asperities)NT total number of grooves (or asperities)p hydrostatic pressures, si interfacial shear strengthS distance slidt microchip thicknessU velocityV, Vh theoretical volume wear rateV actual volume wear rate
semi-asperity angleangle in the hodograph
171, 772, r73 "friction" angles0 angle in the slip line field
ratio of the volume removed to the calculated wear volumeOn normal stressat tangential stressi angle in the slip line field)shear angle in Henky's equations
Subscriptsa actualth theoretical
74
